Random optical bipolar pulses (ROBPs) were experimentally demonstrated in an all-optical continuous wave stimulated Brillouin scattering system without any modulation. The features of these bipolar pulses include short rise and fall time, different recurrence rates, and double-frequency property. Three-wave parametric coupling equations model simulations agree qualitatively well with the experiments. Our experimental and theoretical studies confirm that the optical feedback is essential and the multi-wave coupling effects are the mechanism for the ROBPs events.