Bulger, who's 84, was convicted and sentenced on racketeering charges that tied him to 11 murders and other gangland crimes from the 1970s and '80s.
In an appeal filed Thursday in the 1st U.S. Circuit Court of Appeals, Bulger's lawyers Henry Brennan and James Budreau argue he was "deprived" of a critical defense in his trial: that a now-dead federal prosecutor had given him immunity from his crimes.
Bulger had been an FBI informant against the rival New England Mafia, which his lawyers say allowed him to avoid prosecution for almost 25 years while his Winter Hill Gang consolidated power and built a criminal enterprise that took in millions of dollars through drugs, gambling, loansharking and other illegal activities.
Bulger's case ultimately became a black eye for the FBI and the basis for recent Hollywood movies after it was revealed that corrupt federal agents had accepted bribes and protected him over the years.
But, during the trial last year, Judge Denise Casper ruled Bulger couldn't raise the immunity claim because he offered no hard evidence to support it. The judge also said prosecutor Jeremiah O'Sullivan, who died in 2009, didn't have authority to grant such immunity.
This "constitutional error" affected the fairness of Bulger's trial and must result in reversal, his lawyers wrote in their appeal.
"If Mr. Bulger had been permitted to testify about his immunity defense in his own words, then the jury would have the opportunity to weigh his credibility with that of the government's witnesses," they wrote. "... His testimony alone could have made a difference in the verdict."
Bulger's lawyers also argue they had been prevented from showing how the government's plea deals with three key witnesses - a gangster, a hit man and a Bulger protege - "deeply inspired" the former associates to blame their boss for "any and all crimes, regardless of the truth."
Bulger's lawyers hone in on hit man John Martorano, who admitted killing 20 people but served only 12 years in prison in exchange for testifying against Bulger.
Bulger's lawyers say they should have been allowed to explore allegations Martorano had been committing new crimes since his release from prison. Prosecutors have said the allegations had been investigated and found untrue.
Bulger fled Boston shortly before his 1995 indictment after being tipped off by a former FBI agent. He was one of the FBI's most wanted fugitives for 16 years until his 2011 arrest in Santa Monica, California.
Following a 35-day trial, a federal jury last August found Bulger guilty of 31 of 32 counts, including racketeering, money laundering, extortion and firearms violations.
The jury also found prosecutors had proved Bulger participated in 11 of the 19 murders of which he was accused. Bulger was sentenced in November 2013.