There are two possible terminations for the ideal NiAl(111) surface, i.e., all Al or all Ni on the surface atomic layer. We investigate which termination occurs on the NiAl(111) surface by comparing the pseudopotential electronic band structure of a Ni-terminated and an Al-terminated NiAl(111) surface with the angle-resolved photoemission data on a NiAl(111) sample. The measured surface band structure shares common features partly with that of the Ni termination and also partly with that of the Al termination, which supports the theory that the real NiAl(111) surface is composed of both Ni- and Al-terminated (111) domains, as suggested by a recent low-energy electron diffraction (LEED) study. We also determine the relaxation of the two outermost atomic layers for both terminations by the pseudopotential total-energy calculations and compare them with the LEED results. We find that the present results are in good agreement with the LEED analysis for Ni termination, but in qualitative disagreement for Al termination.