A multi-phase motor control apparatus that reduces the occurrence of the vibrations and the noises by setting the shift amount per time more finely after realizing a reduction in processing ability of a CPU by using a one-shunt type current detection circuit and an electric power steering apparatus using the same. The apparatus includes a PWM-signal generating section that generates plural second each-phase PWM-signals within two control periods based on the current estimation value and the carrier signal, and in a case that a phase shift amount of a predetermined phase in a just before control period is zero and a phase shift amount of a predetermined phase in a present control period is not zero, the phase shift control section gradually increases the phase shift amount from zero in the present control period and a next control period, and uses the second each-phase PWM-signals in the next control period.