This paper proposes a new outer-rotor fault-tolerant permanent-magnet vernier machine for electric vehicles. It can offer the advantages of high torque density, low-speed high-torque operation and inherently negligible coupling between phases, namely fault-tolerant characteristic. The key of the proposed machine is to newly introduce the flux-modulation poles which can effectively modulate the high-speed rotating field of the armature windings and the low-speed rotating field of the permanent-magnet (PM) outer rotor. In addition, single-layer and multi-phase fractional slot concentrated windings are adopted to improve fault tolerance. For the proposed machine, the relationship among the numbers of the stator slots, winding poles and PM pole pairs are analyzed and discussed. By using the time-stepping finite element method, the electromagnetic performances and the efficiency of the proposed machine are analyzed, verifying the effectiveness of the theoretical analysis.