Christos Pappas refused to turn himself in after the ruling on Thursday, meaning he is officially considered a fugitive.
Thirty-nine members of the neo-Nazi group were convicted of running it as a criminal organisation and later sentenced to prison, including 13 ex-parliamentarians. Others received suspended sentences.
All but two of the 39 turned themselves in. Pappas is on the run; the other is Ioannis Lagos, a European parliament member who lives in Brussels and is protected by immunity.
Pappas' lawyer told Greek state broadcaster ERT that his client would not surrender himself because he believed his conviction would be quashed on appeal, meaning he would serve a prison sentence that could be overturned.
Prosecutors previously descriped the 58-year-old Pappas as second-in-command to Golden Dawn’s leader, Nikos Michaloliakos, who has also been jailed for 13 years.
Thursday’s ruling brought an end to a five-year trial which helped seal Golden Dawn’s downfall. The party, once the third-most popular in Greece, has become riven by in-fighting and failed to win any seats in last year’s parliamentary elections after reaching its peak in 2012.
However, the Greek prime minister has warned that other extreme right-wing groups are filling the space left by Golden Dawn.
“The trial of racism, intolerance and violence in society remains ongoing” even though the verdict “closes a traumatic cycle” in Greece’s history, said Kyriakos Mitsotakis.
Golden Dawn was founded in the 1980s and remained on the fringes until Greece’s extended financial crisis that spanned the last decade.
A crackdown against the group was triggered by the murder of 34-year-old anti-fascist rapper Pavlos Fyssas in 2013, for which Yiorgos Roupakias, a Golden Dawn sympathiser, has now been sentenced to life in prison.
Additional reporting by Associated Press