The club will seek €8.5 million ($NZ13.7 million) from the Brazilian striker, it said on Tuesday (local time).
It is also demanding he returns the loyalty bonus he received after he renewed his deal in October, less than a year before signing with Paris St Germain
The Catalans are asking for an additional 10% payment due to a delay in their demands being met, after presenting Neymar with them on August 11.
"Barcelona have taken these actions in defence of their interests, after Neymar's contract was rescinded just a few months after he signed on until 2021," a club statement said.
PSG signed Neymar for a world record €222 million ($NZ358 million) fee in August, paying his release clause with Barcelona unwilling to negotiate the sale of one of its best players.
Barcelona has passed the complaint to the Spanish football federation (RFEF) after first filing the lawsuit in court, as well as demanding PSG subsidise it, should Neymar not be able to take responsibility for it.
In the days after he signed for the French club, Barcelona refused to pay the reported €26 million ($NZ42 million) instalment of the loyalty bonus which he was due to receive this summer, citing breach of contract.
On Sunday, Neymar criticised the Barcelona board after helping PSG beat Toulouse in Ligue 1.
"I do have something to say, that I am disappointed with them [Barcelona directors]. I spent four very happy years there and left happy, but not with them. For me they shouldn't be in charge of Barcelona. Barca deserve much better and everyone knows this."
