The High Court in Perth has refused to hear an appeal by Gina Rinehart against a decision locking her out of a stake in an iron ore project in the Pilbara.

Lawyers for Mrs Rinehart's company, Hancock Prospecting, wanted the court to hear its challenge to previous court rulings, which ordered the company to turn over its 25 per cent stake in the Rhodes Ridge project to the Wright family.

Peter Wright was the business partner of Mrs Rinehart's father, Lang Hancock, and the legal fight stemmed from an agreement they made in the 1980s about the division of their assets.

Today, the High Court ruled there were no grounds for it to hear Hancock's appeal.

The decision means the Wright family will hold a 50 per cent stake in Rhodes Ridge, with Rio Tinto owning the other 50 per cent.

In a statement, the company Wright Prospecting said it was pleased today's decision upholds its rights.