An electric power steering apparatus of vector control system that calculates steering assist command values of dq axes based on at least a steering torque, calculates dq-axes current command values from the steering assist command values, converts the dq-axes current command values into 3-phase duty command values, driving-controls a 3-phase brushless motor by an inverter of a PWM control, and applies an assist torque to a steering system of a vehicle, wherein the electric power steering apparatus has plural dead time compensating functions of which efficiencies to respectively perform a dead time compensation of the inverter are different each other, and performs the dead time compensation by gradually shifting from one of the plural dead time compensating functions to an another dead time compensating function while mixing the plural dead time compensating functions.