The bird and a female peahen belonged to Riley Richards' daughter and lived at their home in Cypress, Texas, KHOU-TV, Houston, reported.
"My wife and I call him 'Meanie,'" Richards said.
Richards said the peacock had been attacking people, especially women, since its arrival several months ago.
Richards' neighbor, Billie Rumsey, decided she had had enough when the bird went after her again Wednesday.
"When you have a big bird up that high and you're coming out the patio door and that bird comes down on you, it's terrifying" she said.
Rumsey tried calling Harris County animal control and was told they did not deal with birds. She said she also tried to get help from at least two animal rescue groups without result.
She finally called the Harris County Sheriff's Office, which sent a deputy.
The deputy tried using a stun-gun on the peacock, which did not appear to affect it. Riley then asked the deputy for permission to shoot the bird and got it.
Rumsey said the outcome was not the one she was hoping for.