The Brillouin random fiber laser (BRFL) suffers from high intensity noise that comes mainly from longitudinal mode beating at different mode frequencies. In this Letter, we propose and demonstrate that the mode characteristic of BRFL can be manipulated by distributed random feedback, which acts as the longitudinal mode filter. A theoretical model is developed for the first time, to the best of our knowledge, to analyze the mode characteristics of BRFL with different lengths of a weak fiber Bragg grating (FBG) array. In experiment, a single FBG, weak FBG array (reflection of $ - {40}\;{\rm dB}$-40dB) at various lengths, and a Rayleigh scattering fiber are used to provide the random feedback. Both theoretical analysis and experimental results show that single longitudinal mode operation can be realized with the distributed random feedback interferometer, leading to a stable temporal intensity output of the BRFL in the time domain.