The Concerned Citizens of Canberra lost a long-running battle against the mosque when a challenge was thrown out of ACT Supreme Court in July.

That decision cleared the way for the mosque to be built on The Valley Avenue, after a fight that began in August 2012.

The 500-capacity mosque was approved by the city's planning authority that year, but was met with strident opposition by the Concerned Citizens of Canberra.

The group missed the deadline to appeal the court's decision.

A solicitor acting on their behalf, Robert Balzola, on Wednesday applied to seek permission to lodge an appeal after they missed the cut-off date.

The application will be heard on November 14.

Group members delivered thousands of flyers to Gungahlin homes which urged residents to oppose the development because of its "social impact", "public interest" and concerns about traffic and noise in 2012.

The group then took planning authorities to court, first disputing the government's refusal to extend the public consultation period and later extending its action to the decision to approve the development.

But in July, Supreme Court Master David Mossop found the group had no standing to challenge either decision, and wouldn't have won even if they had demonstrated standing.

The court dismissed the group's case and awarded costs against them.