In the opening scene, Ralph "Papa" Thorson (Steve McQueen) arrives in a small town in Illinois where despite being a terrible driver of cars (a running joke used throughout the film), he captures fugitive Tommy Price (LeVar Burton) for fleeing on his bail. Next, Thorson drives to Houston where he is to bring in a dangerous punk, named Billie Joe, whose kinfolk include Sheriff Strong (Ben Johnson), a corrupt redneck lawman who warns Thorson not to get involved. Papa ignores him and ends up in a violent fight with the fugitive, who is so huge, even a beanbag stun gun barely stops him.
Thorson drives both Tommy Price and Billie Joe back to Los Angeles, where he collects his $1,800 reward for bringing them back. However, Thorson vouches for Price, and thus soon after becomes one of his many acquaintances who hang out at Thorson's house.
At home, Thorson is revealed to be an old-fashioned guy who has a love of antiques and classical music, drives a 1951 Chevy and keeps an antique gasoline pump in his house. His schoolteacher girlfriend Dotty (Kathryn Harrold) is pregnant and would like "Papa" to be there for her when the baby is born, but his work continually keeps him on the road.
Thorson works for elderly and veteran bail bondsman Ritchie Blumenthal (Eli Wallach) who sends him out on dangerous assignments to chase down fugitives in all parts of the USA. However, Thorson himself is pursued by a psychotic killer who was one of Thorson's former convicts, Rocco Mason (Tracey Walter), who begins stalking Thorson at his home and begins following Dotty around as well.
Thorson's adventures continue when he is sent to rural Nebraska to bring back two fugitives, called the Branch Brothers. He flies out to Nebraska and ends up with a fancy 1979 Pontiac Trans Am hire car, which he struggles to drive. He heads to the Branch farmhouse where the two psycho brothers steal his car and try to kill him with dynamite. Thorson commandeers a combine machine and chases after the two Branch Brothers through a cornfield, which ends when a stick of dynamite dropped by them blows up their car, but they both survive. Thorson arrives back at the local airport with the destroyed Trans Am on a trailer, and brings the Branch Brothers on a plane back to Los Angeles.
Meanwhile, Rocco Mason begins terrorizing Dotty at her workplace which leads Thorson to try to protect her, but she instead tries to make him give up his bounty hunter way of life and to take her to a Lamaze class. Thorson grows tired of it and Dotty threatens to leave him due to his uncertain feelings towards being there for her.
When Thorson's police friend Captain Spota (Richard Venture) commits suicide after he is investigated for dealing illegal drugs from the Department's evidence rooms, Thorson goes into a further decline.
Blumenthal next sends Thorson to Chicago to pick up fugitive Bernardo (Thomas Rosales Jr.) a dangerous ex-con which leads to a long chase sequence as Thorson and Bernardo exchange gunfire with each other at an apartment building. Thorson chases Bernardo on foot through the streets and to an elevated train where Thorson is forced to climb on the roof of the train to avoid getting shot at. The chase leads to the Marina City complex where they both steal cars and chase each other to the top level the parking garage, where the psychotic fugitive drives off the edge and plunges several stories into the Chicago River to his apparent doom.
After returning to Los Angeles that evening, Thorson learns from Price that Dotty has been kidnapped by Rocco Mason and is holding her at the high school where she teaches. Thorson arrives when Mason attempts to kill him with an M-16 assault rifle. Unarmed after being deprived of his weapon, Thorson lures Mason into one classroom where he floods the room with flammable gas where once Mason opens fire, the sparks ignites the gas and blows up the room with Mason in it.
Having dealt with Mason, Thorson immediately needs to rush Dotty to the hospital when she begins to go into labor. Despite his poor driving skills, he manages to get to the hospital where he collapses, exhausted, in the lobby. He comes to in the final scene to walk back outside where Dotty has given birth and he holds his new baby.
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