A complex-coefficient microwave photonic filter with continuous tunability is proposed and demonstrated, which has a compact structure and stable performance without splitting the optical path and tuning the polarization state. By only controlling the DC biases of the modulator, the amplitudes and the phases of the filter taps can both be tuned. The phase difference between the two filter taps covers a full 360° range from 10 GHz to 32 GHz. Frequency responses of the proposed filter are measured within 10–20 GHz with different center frequencies.