A multi-phase motor control apparatus comprising: a driving section comprising pairs of upper-stage arm switching elements and lower-stage arm switching elements, and driving a multi-phase motor; a single type current detection circuit detecting current values of said multi-phase motor; a PWM-signal generating section generating plural first each-phase PWM-signals in each control period within two control periods based on said current values detected by said current detecting circuit and a carrier signal; a phase shift control section shifting a first PWM-signal of a predetermined phase, which is generated in said PWM-signal generating section, by gradually changing a phase shift amount, and outputting said shifted first PWM-signal to said driving section; characterized in that the phase shift control section is configured to gradually change the phase shift amount within two control periods, and characterized by a current detection observer configured to estimate a current estimation value of said multi-phase motor based on said current values detected by said current detection circuit in a previous control period; wherein said PWM-signal generating section generates plural second each-phase PWM-signals in each control period within two control periods based on said current estimation value and said carrier signal; driving said multi-phase motor in the first control period of said two control periods by using said first each-phase PWM-signals; and wherein 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, said phase shift control section gradually increases said phase shift amount from zero in said present control period and a next control period, and uses said second each-phase PWM-signals in said next control period. a driving section comprising pairs of upper-stage arm switching elements and lower-stage arm switching elements, and driving a multi-phase motor; a single type current detection circuit detecting current values of said multi-phase motor; a PWM-signal generating section generating plural first each-phase PWM-signals in each control period within two control periods based on said current values detected by said current detecting circuit and a carrier signal; a phase shift control section shifting a first PWM-signal of a predetermined phase, which is generated in said PWM-signal generating section, by gradually changing a phase shift amount, and outputting said shifted first PWM-signal to said driving section; characterized in that the phase shift control section is configured to gradually change the phase shift amount within two control periods, and characterized by a current detection observer configured to estimate a current estimation value of said multi-phase motor based on said current values detected by said current detection circuit in a previous control period; wherein said PWM-signal generating section generates plural second each-phase PWM-signals in each control period within two control periods based on said current estimation value and said carrier signal; driving said multi-phase motor in the first control period of said two control periods by using said first each-phase PWM-signals; and wherein 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, said phase shift control section gradually increases said phase shift amount from zero in said present control period and a next control period, and uses said second each-phase PWM-signals in said next control period.