Goofy (Bill Farmer) is a devoted single parent, but remains a source of constant frustration to his teenage son Max (Jason Marsden), who he continually embarrasses with his doting fatherly behavior and obliviously dorky antics. On the last day of school before summer vacation, Max is hopeful about his future and dreams about his crush, Roxanne (Kellie Martin). With the help of his best friends P.J. (Rob Paulsen) and Bobby (Pauly Shore), he makes one last dramatic stab at popularity by crashing the stage at the end-of-school assembly and re-creating a music video of the popular singer 'Powerline.' The live performance is cut short by Principal Mazur (Wallace Shawn) who takes all three boys to the office to await punishment.
While Mazur interrogates Bobby and P.J., Max is approached by Roxanne, who was impressed with his performance. Roxanne's friend Stacy (Jenna von Oy) is hosting a party to watch the upcoming Powerline concert on TV, and Max nervously invites Roxanne to accompany him as his date. Roxanne happily accepts and Max is overjoyed.
Goofy excels at his job as a children's photographer at a local department store, but worries about his strained relationship with his own son. Principal Mazur calls Goofy at work and tells him about Max's prank, exaggerating the facts to make Goofy believe that his son is falling in with the wrong crowd, and that Goofy should keep an eye on Max "before he ends up in the electric chair." Goofy's gruff co-worker Pete (Jim Cummings), who is also P.J.'s father, advises Goofy to take Max on a fishing trip to "strengthen the bond between father and son." Goofy excitedly plans a road trip to Lake Destiny, a boyhood tradition he had shared with his own father.
Max comes home in a fantastic mood, having won the attention of Roxanne and the respect of his classmates. He is confronted by his father, who gleefully tells him of the planned fishing trip, which will take up most of the summer. Max is horrified, as it will cause him to miss the party and his date with Roxanne. He tries to resist, but is forced into the car by his obliviously happy father. Max begs to make a quick stop at Roxanne's house and begins to tell her about the fishing trip, but changes his story, claiming that he and Goofy are going to the Powerline concert and will appear onstage with him. Roxanne takes the bait and excitedly tells him to have a good time. Max is immediately filled with anxiety about how he will back up his lie.
Goofy is so ecstatic to be spending time with his son that he does not notice Max's overt misery. As the long day of driving comes to a close, Goofy takes Max to a bizzare tourist attraction, Lester's Possum Park, which features an animatronic possum puppet show. In view of the other patrons, Goofy embarrasses Max at a whole new level and Max's anger finally explodes. Goofy is hurt and confused as to why his son is so hostile. The next day Goofy attempts to take Max fishing at a campground, and they encounter Pete and P.J. who are camping in a massive RV. Pete's parenting style is a sharp contrast to Goofy's. P.J. is conditioned to strict obedience to his father. Pete tells Goofy to be firmer with Max, reasoning that "if you keep them under your thumb, they won't end up in the gutter." Goofy finally shows some backbone and orders Max to get his fishing gear and come to the lake with him.
Goofy demonstrates the "perfect cast," a fishing maneuver passed down through the Goof generations. He inadvertently hooks Bigfoot (Frank Welker) on the end of the line, and he and Max are forced to take shelter in their car as the creature trashes the campsite and their luggage. Max and Goofy patch things up with each other, and Goofy falls asleep. Max thinks about his lie to Roxanne, and, despite the guilt he feels about deceiving his father, changes the route on the map so it leads to Los Angeles and the Powerline concert, rather than Lake Destiny.
The next morning, Goofy bequeaths the map to Max, naming him "official navigator" of the trip, while remaining unaware of the alterations Max had made. Max is allowed to choose all the stops along the way, and he and Goofy genuinely enjoy each others company at baseball games, beaches, and theme parks. They stop at a motel for the night, once again running into Pete and P.J. Pete is suspicious of the sudden change in Max and Goofy's relationship, and overhears Max telling P.J. about the altered map. Pete warns Goofy that Max is not being truthful, and tells him to check the map. Goofy at first defends his son, but is shocked when he looks at the map and sees that Pete was correct.
Goofy is saddened and angered by Max's lie, and finally confronts him. A huge argument ensues, during which their car rolls off a cliff and into a river. Max and Goofy fall in as well, and climb onto the roof of the floating car. They assure each other that, despite their differences and frustrations, they will always love each other. To their horror, they see they are heading for a huge waterfall and are unable to keep the car from going over and their camping gear spilling out. Max is saved by the tent, which acts as a parachute, but Goofy falls into the fog below. Max grabs a fishing rod and desperately performs the "perfect cast" his father had taught him. He manages to hook Goofy's pants and pull him to safety.
Back on the road, Max explains his situation with Roxanne, and how he has no way to cover up his lie. To his surprise, Goofy promises to get Max onstage with Powerline at the concert to fulfill his promise to Roxanne. They arrive just as the concert begins, sneaking backstage as they have no tickets. While they evade security, they accidentally tumble onstage. Powerline (Tevin Campbell) is startled, but continues his performance along with Max and Goofy. Max's friends back home see him on TV and Roxanne is delighted.
Goofy and Max finally return home, with their car virtually destroyed. Max asks to stop by Roxanne's house so he can come clean. He humbly explains how he had lied to her before he left because he was afraid she would cease to like him if he did not keep up the charade. Roxanne assures him that she had already liked him. Max shyly kisses her on the cheek. The car explodes on the street, sending Goofy flying and crashing though Roxanne's porch roof. Max proudly introduces his father to Roxanne.