This paper proposes a novel modular relieving-dc-saturation Vernier reluctance machine for electric vehicle application, which integrates the merits of a robust structure, controllable excitation field, strong fault-tolerant capacity, and enhanced torque density, benefiting from its special relieving-dc-saturation design. In the proposed machine, zero-sequence current establishes a modular magnetic path and functions as the dominant excitation source for the torque generation. Especially, slot permanent magnets are introduced into each module, which mitigates the saturation effect in stator core caused by dc-biased flux with the zero-sequence current source. Therefore, the proposed machine can achieve enhanced torque density with relatively high current density. In this paper, the machine structure and operation principle are illustrated in detail, with its electromagnetic performance evaluated by time-stepping finite-element analysis. It is revealed that, due to its relieving-dc-saturation ability, torque density of the proposed machine is enhanced by about 20% with high current density.