Based on the stimulated Brillouin scattering, a variable multi-stopband microwave photonic filter with aperiodic spectral response is designed and experimentally demonstrated. Variable multi-tone pump light is generated and the multi-frequency optical sideband is simultaneously processed by the usage of a programmable electrooptic modulator driven by the radio-frequency signal. The number of stopbands, central frequencies of stopbands and out-of-band rejections of stopbands are controlled by the radio-frequency signal. As the experimental result shows, the spectral response of this microwave photonic filter is aperiodic, and the central frequencies of all stopbands are mutually uncorrelated and irrelevant with the number of stopbands, which can be tuned within 2 GHz to 8 GHz independently. The maximum out-of-band rejection can reach to 49 dB.