This paper presents a method to reduce cogging torque in permanent magnet (PM) machines from dynamic control based on harmonic torque counteract (HTC). We find the possibility of dynamic cancellation of cogging torque and harmonic torque by studying their generation mechanism and period characteristics, and further study the current harmonic injection scheme for cogging torque reduction. Further, two case studies of a integer slot PM machine and a fractional slot PM machine based on finite element analysis well validate the proposed method. Among them, the cogging torque of a 6-slot/2-pole PM synchronous machine is weakened from 932.0mN.m to 56.2mN.m, with a weakening ratio of 94.0%, and the cogging torque of the other with 6-slot/4-pole is weakened from 1.23N.m to 44.21mN.m, with a weakening ratio of 96.4%. The theory of this paper can be extended to PM machines with other different pole/slot combinations and topologies.