James Hurley, 54, took part in an armed robbery in Hemel Hempstead, during which PC Frank Mason was shot.
He pleaded guilty to robbery but denied murder and told the appeal court he was intimidated into keeping quiet by Charles McGhee, who pulled the trigger.
Hurley said he now feels safe to try to clear his name as McGhee died in 2009.
His barrister Joel Bennathan QC is asking the court to overturn the verdict.
Hurley, from Luton, was the getaway driver in the Â£14,000 armed robbery of Barclays Bank when PC Mason was killed with a .45 handgun.
He was convicted of the murder along with gunman McGhee and robber Perrie Wharrie in May 1989 and the three were jailed for life.
Hurley claims he was not aware a gun would be used and had nothing to do with the murder.
The court heard from Hurley and nine other prisoners or ex-prisoners who said McGhee, who died in prison, had admitted Hurley had "not known that guns - or tools - were to be carried in the robbery".
Hurley claims he did not speak up during his trial because he was told not to by McGhee, who was described by witnesses as "powerful within the prison system", a "maniac" and "a volatile person who you would not want to cross".
Mr Bennathan said the court "may be reluctant to disturb so serious a conviction so many years later" but "fresh evidence makes clear that Charles McGhee threatened Mr Hurley to prevent him from giving evidence in his own defence".
He said: "It is submitted that the combination of all the material that is now before the court is so powerful and raises such doubt as to Mr Hurley being guilty of murder that this application and appeal should be allowed."
The case continues.
A man convicted of murdering an off-duty policeman in 1988 has told London's Appeal Court he was stopped from giving evidence in his defence.