The Vernier PM (VPM) machine is known as a high-torque and low speed drive solution suitable for direct-drive applications such as electric vehicles and wind turbines. The Consequent-Pole Vernier PM (CP-VPM) machine is a special structure of VPM that also introduces high torque density as the conventional VPM incorporating significantly lower volume of PM materials. Although many researches and experiment studies, especially in recent years, reported concerning the conventional structure, there are little publications on the CP-VPM machine. The paper presents the electromagnetic principles of modulation flux occurring in CP-VPM machine. The operating quantities are evaluated using analytical equations and compared with the conventional machine performance. It is concluded that the torque density and back-EMF are much larger than the conventional machine and the torque pulsation magnitude is lower. However, the power-factor is undesirably reduced due to higher spatial harmonics distortion of the CP rotor magnetic field and presence of magnetic field components that do not contribute in the flux modulation. Based on the spatial harmonic analysis, design modifications for enhancing the operational characteristics of the CP-VPM machine are proposed and their effectiveness is verified through comparing the 2D-FE results with the results of the conventional VPM machines.