We proposed and demonstrated a high-efficiency Brillouin random fiber laser (BRFL) in a half-open linear random cavity incorporating with a self-inscribed dynamic fiber grating (DFG) for laser frequency stabilization. The DFG can be produced when the ion population distribution along erbium-doped fibers is periodically modulated by two coherent counter-propagating standing waves via the spatial hole-burning effect. Consequently, a BRFL with the linear half-open-cavity exhibited an optimized laser efficiency while the embedded DFG effectively purified the random modes and suppress the frequency drift caused by multiple random mode hopping. With a low laser threshold of 13.9 mW, the laser efficiency of up to 19.3% was observed, which is four times higher than that of the BRFL with a half-open ring cavity. It suggests that the proposed BRFLs could be beneficial to practical applications in fiber-optic sensing and coherent communication