Congress created the fee in 1982 to help pay for a central storage site for nuclear waste to be located underneath Yucca Mountain near Las Vegas.
The Obama administration abandoned the project and the nuclear industry does not think the fee is still needed.
The lawsuit seeks to suspend collection of the fee, levied at a rate of 0.1 penny for every kilowatt-hour consumers pay on electric bills.
The fee brings in $750 million a year for the Nuclear Waste Fund held at the U.S. Treasury, which now has a balance of more than $24 billion.
The lawsuit, filed in the U.S. Court of Appeals for the District of Columbia Circuit, was brought by the Nuclear Industry Institute trade group and 16 of its members, which are mostly utilities that operate nuclear power plants.