Spent Nuclear Fuel On-Site Storage Security Act of 2005

Spent Nuclear Fuel On-Site Storage Security Act of 2005 - Amends the Nuclear Waste Policy Act of 1982 to prescribe guidelines for the transfer of spent nuclear fuel, within six years after enactment of this Act, from spent nuclear fuel pools into spent nuclear fuel dry casks at an independent spent fuel storage facility licensed by the Nuclear Regulatory Commission (NRC) and located at the power reactor site.

Instructs the Secretary of Energy to: (1) make grants to compensate a contractor for expenses incurred in carrying out such transfer; and (2) accept the conveyance of title to a spent nuclear fuel dry cask (including its contents) from the contractor following certification of compliance by the NRC.

Confers upon the Secretary full responsibility (including financial responsibility) for the possession, stewardship, maintenance, and monitoring of all spent nuclear fuel transferred to the Secretary.

Requires the Secretary to accept the conveyance of title to all spent nuclear fuel with respect to which, before enactment of this Act, the NRC has certified that certain contractors have completed transfer to spent nuclear fuel dry casks in compliance with applicable regulations.