Sustainable Shetland said that it will not accept a recent ruling that the Viking project can go ahead, which in turn overruled a decision in the campaign group's favour.
Scottish energy minister Fergus Ewing gave SSE and community group Shetland Charitable Trust the nod to develop the project in 2012. But last October, the Court of Session ruled that the government should not have granted consent.
The judge, Lady Clark of Calton, said that consent could not be given until the project had been issued with an electricity generating licence. There were fears that this could set a precedent as standard practice in the UK sees a project approved before a generating license is granted.
But this decision was, in turn, overruled in the same court, with the three judges also dismissing a ruling that the impact on migratory birds had not been properly taken into account.
It was thought that as a result the way would be clear for the development to go ahead, but the campaign group will now take the case to the Supreme Court in London. No timescale for the appeal has yet been revealed.
Viking Energy, the joint venture between SSE and Shetland Charitable Trust, said in a statement: "We are very confident that the opinion of the three senior judges [in the Court of Session] will be upheld."