Flywheel energy storage systems (FESS) are technologies that use a rotating flywheel to store and release energy. Permanent magnet synchronous machines (PMSMs) are commonly used in FESS due to their high torque and power densities. One of the critical requirements for PMSMs in FESS is low torque ripple. Therefore, a PMSM with eccentric permanent magnets is proposed and analyzed in this article to reduce torque ripple. Cogging torque, a significant contributor to torque ripple, is investigated by a combination of finite element analysis and the analytical method. An integer-slot distribution winding structure is adopted to reduce vibration and noise. Moreover, the effects of eccentric permanent magnets and harmonic injection on the cogging torque are analyzed and compared. In addition, the electromagnetic performance is analyzed, and the torque ripple is found to be 3.1%. Finally, a prototype is built and tested, yielding a torque ripple of 3.9%, to verify the theoretical analysis.