The Baillieu government has failed in its legal bid to overturn a ban by the Commonwealth on its plans to return cattle grazing to the Alpine National Park.

In a judgment handed down in the Federal Court on Friday, Justice Susan Kenny dismissed Victoria's case on all grounds and ordered the state to pay legal costs.

Safely grazing: cattle on the Dargo High Plains in the Alpine National Park. Credit:Justin McManus

The Baillieu government had wanted to run a six-year trial to test whether cattle grazing curbed bushfire risk by reducing fuel loads.

Cattle grazing in the park was banned by the Bracks government in 2005, with compensation paid to grazing families. But cows were returned to the park in early 2011 by the Baillieu government, soon after it won office.