Huguely, a former UVA lacrosse player, was convicted of second-degree murder for killing Yeardley Love.
He was sentenced to 23 years in prison in 2012. His legal team says the judge in Charlottesville should have delayed his trial, when one of his attorneys got sick and had to miss a day and a half of the 12 day long trial.
They also said several jurors should not have been allowed to serve, because they may have had strong opinions about the case.
Huguely's lawyers spoke with CBS 6 as they were leaving court.
It could be months before the appeals court decides whether to grant Huguely a new trial.
“We're certainly confident in the courts and we’re very happy, as I said, that they heard our arguments today,” his lawyer said.