A random fiber laser with stimulated Brillouin scattering (SBS) and erbium-doped fiber (EDF) as hybrid gains was proposed and experimently investigated. Two spools of 20 km long single-mode fibers were used to form a full-open cavity and provide random optical feedback by Rayleigh scattering. For fixed Brillouin pump wavelength and pump power of 1550.00 nm and 2.19 mW, the proposed laser can achieve random lasing of two wavelengths with frequency downshift of about 0.088 nm and 0.174 nm relative to the Brillouin pump wavelength when EDF pump power increases. EDF pump powers corresponding to the 1st and 2nd SBS are 190 mW and 370 mW, respectively. Maximal output powers of two ends are 1.60 mW and 1.68 mW when EDF pump power is 433 mW. When EDF pump power is obviously higher than the threshold power, the output lasing has 3 dB linewidth of about 0.022 nm and keeps stable. The peak intensity and wavelength have no observable fluctuations over time.