The Alliance to Protect Nantucket Sound, helped by constitutional lawyer Laurence Tribe, submitted the brief stating the US District Court Judge's previous ruling was "gravely flawed".
Campaigners previously sued state officials and Cape Wind on the grounds that Massachusetts utility company, Nstar, was forced by state officials to purchase the electricity from the offshore project at a higher price than the market rate.
The judge threw out this lawsuit in May, after he ruled it contravened the US constitution.
A spokesperson for Cape Wind said the project will carry on as planned, despite this latest court process, claiming the Alliance is making the same arguments as before, which the judge rejected.
"Project opponents have now lost 26 legal decisions and with this filing they are heading to 27," the spokesperson added.
Cape Wind could be one of the first operational offshore wind projects in the US. It is planned to be installed in the Nantucket Sound off the coast of Massachusetts.
German manufacturer Siemens has signed a deal with the developers to proivide 130 of its 3.6MW turbines to the project.