A single-longitudinal-mode (SLM) narrow-linewidth Brillouin erbium-doped fiber laser (BEFL) is proposed and demonstrated experimentally. The erbium-doped fiber (EDF) is employed to act as both the linear gain and Brillouin gain medium, which makes it easy to excite the stimulated Brillouin scattering (SBS) in the EDF by cooperating with the ring cavity structure. In order to realize stable SLM and narrow-linewidth laser output, the fiber saturable absorber (SA) and the self-injection feedback structure are added to BEFL for the first time, which can suppress the multimode phenomenon effectively and obtain a stable SLM status. The wavelength stability is less than 1.32 pm over 45 minutes and the linewidth is as narrow as 283 Hz.