Two gas company men are lured by a scantily-clad woman to a remote spot and killed by Bobby Maxwell (DeVeren Bookwalter). Maxwell's gang, the People's Revolutionary Strike Force (PRSF), a self-proclaimed terrorist group made up of several disgruntled Vietnam veterans, who plan to use the gas men's uniforms and van as part of an ambitious series of crimes that will make them rich.
Inspector 'Dirty' Harry Callahan (Clint Eastwood) and his partner Frank DiGiorgio (John Mitchum) arrive at a liquor store where robbers have taken hostages. The robbers demand a car to take them to the airport. Dirty Harry provides one... by driving his squad car into the store and shooting all the robbers.
Afterwords, Callahan's no-nonsense and by-the-book superior Captain McKay (Bradford Dillman) reprimands Callahan for "excessive use of force", injuring the hostages, and causing more than $14,000 of damage to the store, and temporarily transfers him out of the Homicide unit. While assigned to Personnel, Callahan participates in the interview process for promotions, and learns that three of the new inspectors will be female including Kate Moore (Tyne Daly), despite her very limited field experience.
Meanwhile, the PRSF uses the gas company van to steal several M-72 LAW rockets and other weapons from a warehouse, killing DiGiorgio during the robbery. To Callahan's distress, Moore is his new partner. She claims to understand the risk, noting that (besides DiGiorgio) two other partners of his have died in the past five years (in the last two Dirty Harry movies). They visit the Hall of Justice for an autopsy where a bomb explodes. Callahan and Moore chase and capture the PRSF bomber. Later, Callahan and Moore meet "Big" Ed Mustapha (Albert Popwell), leader of a black militant group the bomber formerly belonged to.
Although Callahan makes a deal with Mustapha for information, McKay arrests the militants for the PRSF's crimes. Callahan angrily refuses to participate in a televised press conference in which the publicity-seeking Mayor would commend him and Moore ("one of the first of her sex in the whole country") for solving the case, and the arrogant McKay suspends him from duty. Moore supports Callahan and gains his respect.
But two days later, the PRSF boldly kidnaps the Mayor after a Giants game and demands a $5 million ransom. With Mustapha's help, Callahan and Moore locate the gang at Alcatraz Island, where they land by boat and battle the kidnappers in a climatic shootout, killing all of them exept for Maxwell. Moore frees the Mayor, but Maxwell kills her as she saves Callahan's life. He avenges Moore by chasing after Maxwell who fortifies himself atop an old guard tower, and Callahan kills Maxwell by literally blowing him up with a LAW rocket. Dirty Harry Callahan is uninterested in the pompous Mayor's gratitude, returning to his partner's corpse as McKay and other policemen arrive.