In the waning days of World War II, in the South Pacific, the men of the Navy cargo ship USS Reluctant are hard at work moving supplies and resupplying other ships of the US Navy. The men are led by Lieutenant Doug Roberts, who is well-liked by the entire crew and acts as a liaison between them and their captain, Morton, who is a mean-spirited, exacting and tyrannical officer. Recently the Reluctant was recognized for moving the most cargo of any resupply ship in the fleet. The reward for their efforts is a single palm tree, which was really given to Capt. Morton. The tree is displayed proudly on the foredeck by Morton.
The result of the recognition is that the Captain has become more tyrannical than ever. He stolidly refuses to let the crew have a standard liberty and micromanages Roberts' duty to keep them engaged while they complete their missions.
Roberts himself feels that, knowing the Pacific war is winding down, he'll never have the chance to serve in naval combat. He's also become quite fed up with the Captain's oppressive attitude and has written a number of letters to the Captain requesting transfer to a combat vessel -- requests that have gone unfulfilled by the Captain.
Doug's closest friends on the ship are Ensign Frank Pulver and the ship's doctor, known as Lt. "Doc". Though he likes Pulver immensely, Roberts is quick to point out that Pulver isn't a very effective leader and is a disorganized person in general. Pulver despises the Captain as much as the rest of the crew and talks often about schemes to annoy the Captain but never follows through on them. When he meets the Captain face-to-face one day he cowers before him.
The ship is due to make port at a small Pacific Island, one where there is a full hospital. Pulver sees his chance to find a pretty nurse and possibly woo her. He invites her to tour the ship, however she brings her assistant nurses with her, ruining any chance Pulver has at romance.
Roberts goes over the Captain's head and requests liberty for the crew. The Captain allows the ship to make port at Elysium, an island tropical paradise but announces that the liberty has been cancelled. Infuriated, Roberts storms into the Captain's quarters and demands to know why liberty was cancelled. Morton tells Roberts a bit of his own history: he was a busboy for several years and received poor treatment from his customers. He then became a ship's steward and the poor treatment continued. He sees Roberts, a college graduate, as representative of those who treated him badly as a youth and now seeks to pay them back.
Before he grants the crew liberty, the Captain demands that Roberts quit his efforts to obtain transfer and that he become a model officer, essentially becoming a more by-the-book leader and work the crew to their limits. Roberts reluctantly agrees and the Captain allows the crew to go on liberty.
That night the crew become highly drunk, raucous and destructive on the island. Many of them are arrested and brought back to the ship by Army MPs (in some cases, Roberts lets them go right back out again). The men break into the home of the French Colonial governor and wreak havoc there. A small detachment of Army MPs show up and form a cordon around the ship, preventing any other men from leaving. The commanding officer has requested that Morton see the Rear Admiral stationed on the island in the morning.
Morton returns from his meeting furious -- he and the crew have been ordered to leave port immediately. He commands Roberts to make good on his promise of becoming a stricter officer, which Roberts does. When one of the crew, Dolan, approaches Roberts with what may be good news -- that officers that have a requisite number of months experience may apply for transfer uncontested -- he viciously puts Dolan on report. Upset that he'd had to enforce discipline when a crew member didn't deserve it, Roberts talks to Doc. The Doc tries to reason with Roberts, who stops short of revealing the deal he'd made with the Captain. Just then, Pulver bursts in with the news that Germany has surrendered in Europe. Roberts is overjoyed about the news and Pulver tells him he'll celebrate by putting a powerful firecracker under the Captain's bunk. However, while he gathers his explosives, they go off in the bowels of the ship, causing the laundry to become flooded with soap suds. Roberts is still overjoyed, thinking that Pulver can make another firecracker, however, all of Pulver's supplies were destroyed in the accident. Roberts is very forgiving of Pulver and goes out to be alone on the deck.
On the deck, Roberts listens to the radio broadcast of the victory celebration coming in from New York City. The broadcast then changes to a man giving an inspirational speech about how the war isn't over until it's won in the Pacific. Roberts is moved by the speech and marches up to the Captain's palm tree, salutes it and throws it overboard. When the Captain finds out, he sounds the ship's general alarm which musters the crew to their battle stations. When they've all assembled, he demands to know who destroyed his palm tree. After having his adjutant read the muster list, he determines that Roberts is the culprit. Roberts is called to the Captain's room, but before the Captain can even charge him with the crime, the Captain is overcome with nausea. Roberts calls in Doc to help the Captain, who vomits into his own wastebasket. Doc puts the Captain in his bunk to relax. As Roberts walks down to the deck the crew, knowing that he'd destroyed the palm tree, all salute him and politely bid him goodnight.
A few days later Mister Roberts is packing his things. The Captain has approved a transfer for him and he'll be going to the front line in the Pacific. Before he leaves, Dolan informs him that the Captain has replaced the palm tree and has put a 24 hour guard on it. As he gets ready to meet the transfer vessel, a few of the crew give Roberts a medal they'd made: it is a gaudy brass palm tree with a ribbon. Roberts is overcome with gratitude, pins it to his blouse and walks with dignity out to the boat that will take him off the ship. He salutes the entire crew and leaves.
Several weeks later, Pulver has taken up Roberts' duties as deck officer, managing the moving of cargo. A few of the crew approach him and tell him that the Captain has cancelled the movie that was to be shown that night. Pulver reluctantly tells them he'll do what he can. The ship's mail arrives and Pulver receives two letters. The first he reads is from Roberts, who seems happy that he's finally in the war and that his unit has been involved in a number of air raids. He talks about the brave crew that served him on the Reluctant and the ridiculous ribbon they gave him. The second letter is from a friend of Pulver's who is serving on the same ship as Roberts and has become friendly with him. Pulver's friend writes that their ship suffered a surprise attack and that Roberts was killed while eating a meal. Pulver is overcome with grief and plans to announce the news to the crew. Doc stops the communications officer and tells him to read the letter that Roberts wrote, saying "it belongs to them".
Pulver suddenly becomes enraged and marches up to the palm tree, grabbing it and throwing it overboard. He continues to the Captain's quarters, banging on the door until he's told to enter. Angrily confronting the Captain, he tells him that he'd thrown the palm tree off the ship and demands to know why the movie has been canceled for the evening. The Captain groans knowing that he'll have the same trouble with Pulver that he did with Roberts.