Nie Shubin was 21 when he was executed after being found guilty in 1995 of the rape and murder of a woman on the outskirts of Hebei provincial capital, Shijiazhuang. The application was handed in to the Higher People's Court of Hebei Province in north China, Xinhua news agency reported.
Earlier this month, the Supreme People's Court, China's top court, acquitted Nie, ruling that the previous conviction was based on insufficient evidence and unclear facts.
The family also requested that those who made the initial wrong conviction send a letter publicly apologising for wrongly executing Nie.
Nie's case reemerged in 2005 when another man, Wang Shujin, confessed to the crimes Nie was convicted of. Wang, 49, was given a death sentence in unconnected rape and murder cases.
The Supreme People's Court decided to retry the case in June 2016.