Membership or expressing support for the group is a criminal offence punishable by up to 14 years in prison
The co-founder of Palestine Action, Huda Ammori, can challenge the Home Office decision to ban the group as a terrorist organisation at the Supreme Court, court records show.
The decision sets up a final legal battle with the Home Office this autumn.
The terrorist organisation was proscribed in the UK following a legal battle on July 4 last year.
Membership or expressing support for the group is a criminal offence punishable by up to 14 years in prison.
It has remained in place while the Home Office battled the legal challenge launched in February.
Last month, five of Britain's top judges overturned an earlier High Court decision to lift the ban, stating: "The proscription decision was not unlawful."
The Court of Appeal held that the then Home Secretary, Yvette Cooper, had correctly applied her published policy.
Lady Chief Justice Baroness Carr said that Palestine Action’s ban was "a justified and proportionate interference with individual rights".
She described the group as one that "overtly promotes unlawful violence amounting to terrorism".
Co-founder of the group, Ms Ammori, has been given permission to appeal the ruling.
She has previously branded the decision "one of the most extreme attacks on free speech and the right to protest in modern British history”.
The legal battle began after members broke into RAF Brize Norton and vandalised jets to protest the war in Gaza.
