In this Letter, we report a chip-based photonic radio-frequency (RF) mixer with a maximum conversion gain of -9dB and image rejection ratio of 50 dB for 3.2 GHz to 13.2 GHz RF frequency range. This is achieved by the combined use of optical carrier suppression modulation and on-chip stimulated Brillouin scattering. These results will stimulate future implementations of integrated photonic RF mixers in complicated electromagnetic environments.