Attorney Dylan Schaffer argued at the 45-minute hearing that while Mehserle made a "tragic and horrible error," he didn't act with the level of recklessness that legally defines involuntary manslaughter.
"All he did is make an error," Schaffer told a three-judge panel of the Court of Appeal.
"Police officers are fallible. We cannot put them at risk of prosecution for just making policing errors," Schaffer said.
Mehserle, 30, was convicted of involuntary manslaughter by a Los Angeles jury in 2010. He was sentenced to two years in prison and was released last year after receiving credits that reduced his time in custody to about a year.
Another defense attorney, Michael Rains, said that although Mehserle has completed his sentence, he is pursuing the appeal because he can't return to a job in law enforcement with a felony conviction on his record.
Rains said Mehserle has been working in non-law-enforcement jobs, but declined to give details except to say that the former officer is a talented handyman.
Mehserle, wearing a dark business suit, attended the hearing but made no public comments.
Mehserle claimed after the shooting that he had accidentally used his revolver when he meant to use a Taser stun gun to subdue Grant during the incident at BART's Fruitvale station early on New Year's Day in 2009.
Schaffer argued at today's hearing that there was insufficient evidence to support a finding of recklessness and that there were errors in jury instructions at Mehserle's trial.
Senior Assistant Attorney General Gerald Engler, representing prosecutors, argued that there was "ample evidence" that Mehserle acted recklessly.
Engler listed a series of differences between a revolver and a stun gun. Mehserle was convicted "not because he committed a mistake, but because this mistake was committed with gross negligence," Engler argued.
The appeals court now has three months to issue a written decision. Schaffer said that if Mehserle loses the appeal, he will continue appeals to the California and U.S. supreme courts if necessary.