A switchable and filter‐free photonic microwave single‐sideband frequency converter based on a dual‐parallel dual‐drive Mach‐Zehnder modulator is proposed and experimentally demonstrated. Two first‐order carrier‐suppression single sidebands for input signal and local oscillator signal are achieved by adjusting the DC bias voltages of the modulator. The frequency upconversion and downconversion can be switched by adjusting one DC bias voltage of the modulator. Thanks to the carrier‐suppression single‐sideband modulation without using any filter, the frequency converter has a large operating bandwidth but no power fading caused by chromatic dispersion, and the mixing spurs can be effectively suppressed. Experimental results show that the frequency converted signal is pure over a wide frequency range, and the sideband suppression ratio of desired signal is over 20 dB. The spur free dynamic range achieves 108.3 dB Hz2/3.