The magnetic field dependence of current-induced magnetization reversal was investigated for current-perpendicular-to-plane giant magnetoresistance pillars with perpendicularly magnetized FePt layers. Current-induced magnetization reversal under the tilted external magnetic field showed that a reversed domain is nucleated by spin-transfer torque and then propagates to complete magnetization reversal, although the formation of a multiple-domain state is not observed by static measurement. This nucleation-type current-induced magnetization reversal is characteristic of a system having large magnetic anisotropy and a small number of pinning sites for the domain wall, and explains the large magnetic field dependence of the critical current density for magnetization reversal $({J}_{c})$. As the magnetic anisotropy of the FePt free layer is reduced, the magnetic field dependence of ${J}_{c}$ becomes close to the values theoretically calculated for the coherent rotation mode, implying that the mode of the current-induced magnetization reversal changes from the nucleation of a reversed domain to the rotation of magnetization.