Police identified the man as Steve Stephens and have placed a bounty of $50,000 reward for information leading to his arrest.
Cleveland police were searching for a suspect they said broadcast video of himself on Facebook killing a person on Sunday and claiming that he had murdered others.
The Cleveland Division of Police said it was looking for Steve Stephens in connection with the killing of an individual in the city, whom police did not identify.
"Suspect did broadcast the killing on Facebook Live, and has claimed to have committed multiple other homicides which are yet to be verified," the police said in a statement, referring to social media network Facebook Inc's live-streaming video service.
TRT World's Kate Fisher has more details.
Police said that Stephens might be driving a white or cream-coloured sports utility vehicle.
Actual photo of Steve Stephens, homicide suspect's, actual vehicle. Please call 9-1-1 if seen. Plate not yet available. pic.twitter.com/hn8a8nQEAP— Cleveland Police (@CLEpolice) April 16, 2017
In January, four black people in Chicago were accused of attacking an 18-year-old disabled white man and broadcasting the attack on Facebook Live while making anti-white racial taunts. The incident prompted international outrage.
A month later, the accused pleaded not guilty to assaulting the man, whom prosecutors described as schizophrenic.