Due to nonlinear loads and shunt power-factor-correction capacitor in power distribution system, harmonic distortion and harmonic resonance could be caused, which would seriously deteriorate the power quality. Shunt active power filters (SAPFs) only compensate the harmonic currents or suppress harmonic resonance, which may not be sufficient to meet a good power quality. This paper investigates harmonic suppression and resonance damping combined control for SAPF with selective closed-loop regulation of PCC voltage. Firstly, a recursive discrete Fourier transform (RDFT) algorithm is utilized to extract the harmonic suppression current reference from nonlinear load. Then, a novel selective closed-loop regulation of PCC voltage is proposed to damp harmonic resonance. Meanwhile, a zero steady-state error control strategy composed of ordinary PI controller and advanced repetitive controller in parallel under synchronous rotation frame is adopted to improve the output current tracking accuracy of SAPF. Finally, a lot of simulation and laboratory test results are provided to verify the effectiveness of the suggested control tactics.