We propose and experimentally demonstrate a scheme of high-Q microwave photonic filter (MPF) using the techniques of self-phase modulation (SPM) spectrum broadening and third-order dispersion (TOD) com-pensation. The optical pulses from a mode-locking laser are spectrally broadened by the SPM in the highly nonlinear fiber. A wideband optical frequency comb with 365 spectral lines within 10-dB power variation from the highest spectral power is obtained. By applying a cubic phase modulation via a waveshaper, the effect of TOD which broadens the MPF passband is eliminated. The final implemented MPF has a Q-value as high as 296 and a tuning range of 700 MHz.