The Premier League club argue there was a "clear error" in the decision-making process.
Arsenal have applied to double the number of concerts from three to six at their north London stadium.
Opponents have voiced concerns over noise and rowdy music fans. Concerts featuring Bruce Springsteen, Coldplay and Muse have generated hundreds of thousands of pounds extra revenue for the club.
Islington Council rejected Arsenal's application and a planning inspector dismissed the club's appeal in January this year.
The inspector said that if Arsenal could afford to buy a player like midfielder Mesut Ozil for £43million from Real Madrid in the summer, they could not plead poverty.
But on Tuesday Dan Kolinsky. representing the club, told Mr Justice Cranston at the High Court in London the inspector's decision was legally flawed and should not be allowed to stand.
Applying for judicial review, Mr Kolinksy submitted the inspector had failed to apply the law correctly when he decided the proposal to double the number of concerts "did not accord with the development plan" for the stadium.
He told the judge: "We say there is a clear error on the face of the decision letter."
Lawyers for the inspector and Islington are arguing the inspector followed the correct approach and there is no substance in the club's challenge.
During the public inquiry run by the inspector, Arsenal chief executive director Ken Friar said the club needed the money from the gigs to perform in the extremely competitive world of football, citing Manchester United's profits at £100m compared to Arsenal's £20m.
- Sports & Recreation
- Bruce Springsteen