The effect of the perpendicular field on the trajectory of a vortex core driven by spin-transfer torque was investigated using micromagnetic simulations. The trajectory of the vortex core was staggered due to distortions of the moving vortex core. The core trajectory was affected by both the perpendicular field and ${eta}$ value, which is the relative magnitude of nonadiabatic spin torque to the adiabatic spin torque. This suggests that the effect of the perpendicular field should be considered when examining a vortex core trajectory affected by ${eta}$.