Using atomistic empirical pseudopotentials, we have calculated the electronic structures of CdSe nanowires with a bulged area. The localized state wavefunctions and their binding energies are calculated, and their dependences on the bulged area shape are analyzed. We find that both the binding energy and the wavefunction localization strongly depend on the bulged area shape, with the most compact shape produces the largest binding energy and strongest wavefunction localization. We also find that the top of the valence band state has a weaker localization than the bottom of the conduction band state due to an effective mass anisotropy.