The disc coreless permanent magnet synchronous motor has the advantages of a short axial size, high power density, and small volume. Due to the coreless structure, its inductance is very small, which results in a serious current ripple and an unacceptable torque ripple if driven from a conventional inverter. This can be solved by installing an LC filter between the inverter and the motor. However, an undesirable resonance phenomenon is induced by the LC filter. In this paper, a new capacitive current feedback active damping (CCFAD) strategy is proposed. Instead of current sensors in the capacitor branch, a state observer is introduced to estimate the capacitance current. The observer is designed with double sliding mode surfaces, which reduces the order of the system. Compared to conventional capacitive current feedback, no additional current sensors are required, reducing the system cost. Besides the resonant harmonics, the phase current contains obvious fifth and seventh harmonics due to the special plane structure of the rotor. The proportional-integral-resonance (PIR) controller, instead of the traditional PI controller, is designed to suppress lower order harmonics. The experiment results show that current ripples due to resonance and rotor structure are suppressed significantly.