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Seamus Kearney was found guilty last December of killing RUC Reserve Constable John Proctor as he visited his wife and new-born son in hospital.
Kearney's lawyers claimed he was wrongly convicted on the basis of DNA on cigarette butts found at the scene.
The Court of Appeal upheld the DNA evidence and dismissed his appeal.
The three Appeal Court judges ruled that the judge in the original non-jury trial was entitled to conclude the stubs were smoked and discarded immediately prior to the shooting.
Rifle
Kearney, 57, of Gorteade Road, Maghera, County Londonderry, was sentenced to at least 20 years in jail last December for the murder carried out in September 1981.
Mr Proctor, a 25-year-old Royal Ulster Constabulary (RUC) Reserve Constable, was shot dead by the IRA minutes after visiting his wife and newborn son at the Mid Ulster Hospital in Magherafelt.
Kearney had denied murder and possessing an Armalite AR15 rifle.
But the trial judge found him guilty after hearing key evidence that his DNA profile was on a cigarette butt found among spent bullet casings at the scene.
Kearney was found to be either the gunman, the driver of a Ford Escort RS200 used by the killers, or an occupant of the car present to provide support.
Even though Kearney is expected to serve only two years of his jail term under the terms of the Good Friday Agreement, he mounted a challenge to both the conviction and sentence.
The prosecution argued that his refusal to enter the witness box at his trial strengthened its case that he had no innocent explanation for the DNA match.
Notebook
Appealing the conviction, defence counsel questioned the evidence that was said to show the two retrieved cigarette ends were discarded at the time of the shooting, rather than some significant period beforehand.
It was contended that a description of the butts as being clean and fresh, given in evidence by a police constable who seized them, was accepted without any notebook entry on their condition at the time of recovery.
But Mr Justice Weatherup, sitting with Lord Justices Girvan and Coghlin, held that there was nothing inconsistent with the cigarette ends having been discarded immediately prior to the shooting.
"He (the trial judge) was entitled to find the appellant's DNA arose from the appellant smoking the cigarette and then discarding the butt in the car park," Mr Justice Weatherup said.
Backing the decision to admit Kearney's later conviction for possession of a rifle used in a gun attack on a Ulster Defence Regiment (UDR) patrol in 1982, the court held that it demonstrated probative force.
Kearney's failure to offer any alibi for the DNA find was also properly used to draw an adverse inference, according to the three judges.
Mr Justice Weatherup said: "There was no basis for concluding that the passage of time would have prejudiced the appellant in offering an innocent explanation.
"We are satisfied that the appellant's convictions are safe. The appeal is dismissed."