An extreme solar cosmic ray event broke out on 2005 January 20. Not only is it the most intensive solar energetic particle (SEP) event, with >100 MeV particles measured by GOES satellite since 1986, but it has been the largest ground level enhancement (GLE) event recorded by the ground-based neutron monitors since 1956. This work presents the solar proton spectra for this event with data obtained by GOES in multiple energy channels. These spectra are well fitted by a modified power-law function. The spectral index of around -1 indicates that the January 20 event has a hard energy spectrum. Possible mechanisms for the acceleration of relativistic protons are discussed.