The play begins in 1957. Troy Maxson and his friend Jim Bono share stories and a bottle of whiskey on a Friday night. Troy's wife, Rose, tells Troy that their son Cory is being recruited to play college football. Troy is disgusted with the idea. Troy had once been a star in the Negro Leagues, but he was heartbroken by his barrier from the majors. He sees no better future in sports for his son. His older son Lyons stops by to ask his father for money; Troy is not pleased that Lyons is a struggling musician, but he accepts that Lyons is his own man and is making his own way in life.
The next day Troy and Rose get into an argument over his son's apparent laziness. Rose tells him that he has gone to football practice. Gabriel Maxson enters. He is Troy's brother. Gabe suffered a head injury in World War II and now believes he is the angel Gabriel. He carries a trumpet around his neck to blow and open the gates of heaven. Gabe has recently moved out of Troy's house and into his own apartment, something he is very proud of. It is soon learned that Troy used Gabe's disability wages from the Army to buy his house.
A few hours later, Cory returns from football practice. Rose tells him that Troy is furious that he did not help him build the fence in the yard. Their conversation turns contentious after Troy asks Cory about his football scholarship and his job at the A&P. Troy demands that he quit the team and get back his job at the grocery store. After Cory leaves, Troy tells Rose that he doesn't want his son to be like him in any way. She tells Troy that Cory just wants to hear that he has done a good job, but Troy says he can give no more than he already does to his family.
Two weeks later, Troy and Bono come home from work and report how Troy confronted his boss and received a promotion to be the driver of the garbage truck. Troy tells the story of his own father, and how his father beat him and kicked him out of the house at fourteen years old. Troy hates his father but respects his sense of responsibility to his family. After coming to Pittsburgh as a young man, Troy killed a man while trying to rob him and went to prison for fifteen years. This is when Lyons was born. Cory returns from his football practice and is upset because his coach told him he couldn't play. Cory knows that Troy went to the coach to have him kicked off the team. He and his father argue, and Troy tells him that he shouldn't strike out with him.
The next morning, Cory stands by the tree in the yard and practices his baseball swing, but he is more awkward than his father. Troy returns from the police station after having been called to bail out Gabe for disorderly conduct. Bono and Troy begin to build the fence and Bono chides Troy for his scandalous relationship with a woman named Alberta. Bono implores Troy to hang onto Rose. When Bono leaves, Troy admits to Rose that he is having an affair and that he is fathering an illegitimate child. Rose tries to explain how she worked to be a good wife and mother to him and his child. Troy insists that he has done nothing wrong except follow his own desire. She tells Troy that he takes a lot from her and this makes him angry. He goes towards Rose and Cory steps in and shoves Troy. Troy almost retaliates violently before Rose stops him and Troy tells Cory not to strike out.
Six months pass by. Troy is going to see his newborn child when the hospital calls - Alberta has died in childbirth. Troy is enraged and begins engaging a personified Death in conversation. He assures death that he will closely guard everything that belongs to him. A few days later, Troy comes home with his baby in his arms. He pleads with Rose to care for the child even while he remains unapologetic for his infidelity. Rose accepts the child but rejects Troy.
Two more months pass by. Cory has graduated and is now looking for a job. Troy initiates a confrontation with him. Cory tells Troy that he doesn't count in the house anymore. They have a physical fight and Troy wrestles the baseball bat away from Cory. Instead of hitting him, Troy kicks him out of the house. As Cory leaves, Troy again taunts death.
Eight years pass. It is 1965 and Rose, Lyons, and Bono gather in the Maxson home for Troy's funeral. Rose has been raising Raynell, Troy's daughter. Cory comes into the yard dressed in a Marine's uniform. It is the first time he has been home in eight years. He and Raynell sit on the front porch and sing Troy's old blues song about his dog, Blue. Cory tells Rose that he is not going to Troy's funeral but Rose tells him he must make peace with his father now.
Gabe enters the yard. It had been uncertain as to whether the mental institution where he lives would let him come, but he arrives with his trumpet, ready to blow Troy into heaven. He tries to blow the trumpet but no sound comes out. Undeterred, Gabe starts to dance, pushing Lyons away from him. As he dances, the gates of heaven open for Troy and Gabe tells them all, "That's the way that go!"