A mentally ill African American man has spent more than three decades in the US state of Texas without conviction, a defense attorney says.

Jerry Hartfield, 59, has been jailed for over 35 years despite his original murder conviction being thrown out from being found guilty, defense attorney Jay Wooten told jurors on Wednesday, the Associated Press reported.

Hartfield faces life in prison if convicted of capital murder the killing of 55-year-old Eunice Lowe in September 1976 in Bay City, about 100 miles (about 161 kilometers) southwest of Houston.

Jurors received the case on Wednesday. Hartfield could be found guilty of a lesser charge of murder or could be acquitted by jurors.

"A lot of things are missing from this case," Hartfield's lead attorney, Wooten, said in closing arguments. "Like anything you have at your home since 1976, there are parts missing, there are parts that no longer fit."

A jury threw away Hartfield's original 1977 conviction after hearing an appeal in 1980. After three years, Governor Mark White commuted his sentence to life, but federal courts recently ruled the governor didn't have a sentence to commute.

According to a study, one in every 25 death row inmates in the United States is innocent. Approximately 3,000 US prisoners are waiting to be put to death.

African Americans are also far more likely to be arrested and imprisoned by police than any other racial group, according to a recent analysis by USA TODAY.

Experts say the dramatic gap in arrest and prison rates reflects biased policing as well as the vast economic and educational inequalities that plague much of the US.

In November last year, two black men imprisoned in the US for nearly 40 years for a murder they did not commit were freed.

Ricky Jackson, 58, and Wiley Bridgeman, 61 were both exonerated in a 1975 murder after a key witness against them, who was 13 years old at the time, admitted in 2013 that he lied during his testimony.