Former Govs. George Deukmejian, Pete Wilson and Gray Davis announced the proposed initiative Thursday.
"Old age should not be the leading cause of death on death row," said Wilson.
The measure would limit appeals available to death row inmates, remove the prisoners from special death row housing, and require them to work at prison jobs in order to pay restitution to victims.
In 2012, 53 percent of California voters rejected Prop 34, which would have repealed the death penalty. Officials say now the appeals process needs to be reformed so that it's shorter and less costly.
"No more frivolous appeals, like Kevin Cooper in my county, who murdered a family after escaping from Chino prison, who has been on death row for over 30 years," said San Bernardino District Attorney Michael Ramos.
Former Gov. Gray Davis pointed out that it is also common for an inmate who has just been sentenced to death to have to wait five years before being assigned an attorney.
"That's unacceptable. That means nothing is happening for five years," said Davis.
Kermit Alexander is a former NFL player. In 1984, gang members in South Los Angeles murdered four members of his family -- his mother, sister and two nephews. The killer, Tiequon Cox, went to the wrong house. The intended targets lived two doors away. Cox is still on death row.
"We've been waiting over 30 years for justice. I am terribly, terribly disappointed in our system of justice," said Alexander.
Former L.A. County District Attorney Gil Garcetti is against the initiative, calling it a "misguided effort." He says the death penalty is not a deterrent to crime.
"People have changed. They understand that the death penalty serves no useful purpose. If this initiative were to pass, it's going to take years and years of litigation and millions of taxpayer dollars," said Garcetti.
Executions have been halted since 2006 because of lawsuits in federal and state courts over changing a three-drug lethal-injection method that had been used to carry out death sentences.
The Associated Press contributed to this report.