Helen Duncan, from Callander, near Stirling, was convicted at London's Old Bailey under the Witchcraft Act in 1944 after she revealed Second World War military secrets during a seance.
The medium was arrested in Portsmouth after holding a seance in 1941 in which she claimed to be contacted by a dead sailor from HMS Barham. The battleship had sunk after being torpedoed off the coast of Egypt just days before - but news of its sinking was not officially revealed to the public by the military until 1942.
Miss Duncan was sentenced to nine months in prison after being found guilty under section 4 of the Witchcraft Act 1735, but campaigners say she was wrongly convicted.
Former lawyer Graham Hewitt, who says he is acting on behalf of Miss Duncan's grandchildren, said he would be calling for a new review of the case. Mr Hewitt, assistant general secretary of the Spiritualists' National Union, said he had identified 96 mistakes made in the original trial.
Previous efforts to clear Miss Duncan's name have been unsuccessful, with the Scottish Government rejecting a petition to pardon her in 2008. Attempts to open a judicial review into the case also failed due to a lack of new evidence.
A spokesman for the Criminal Cases Review Commission said: "If Mr Hewitt wishes to send a fresh application to the commission then he is more than welcome to do so."