We propose and experimentally demonstrate a continuously tunable all-optical microwave filter based on a photonic crystal (PC) L3 cavity. Due to the small cavity mode volume and prominent optical properties, the required power to arouse the cavity nonlinear effects is low as microwatt level. Moreover, the cavity resonance could be continuously shifted by finely adjusting the input powers. Therefore, under optical single sideband modulation, the frequency interval between the optical carrier and cavity resonance could be controllable. In this case, the central frequency of the microwave photonic filter (MPF) could be continuously tuned with low power consumption. To the best of our knowledge, the experimental tuning efficiency of 101.45 GHz/mW is a record for on-chip tunable all-optical microwave filters. With dominant features of all-optical control, ultra-high tuning efficiency (101.45 GHz/mW), large rejection ratios (48 dB) and compact footprint (100 µm2), the proposed silicon nanocavity is competent to process microwave signals, which has many useful applications in on-chip energy-efficient microwave photonic systems.