A new microwave photonic filter based on stimulated Brillouin scattering was proposed. By tuning the center wavelength of the optical filter, the switchability between the microwave photonic bandpass filter and the microwave photonic notch filter can be obtained. The passband or the notch center frequency of the microwave photonic filter can be tuned continuously by tuning the wavelength of the pump laser. Since no electrical component was involved, the microwave photonic filter was all-optical. Therefore it can achieve a very broadband operating frequency range. The maximum measured tuning frequency range in the experiment was limited by the displaying range of the vector network analyzer. Since an optical phase modulator was used, no bias voltage was needed. Therefore, there was no bias voltage drift problem. Experimental results demonstrate a switchable and continuously tunable microwave photonic filter with a broadband operating frequency range from 9-26.5 GHz. The bandpass filter has a narrow 3 dB bandwidth up to 28 MHz, which is limited by the optical fiber Brillouin gain linewidth.