A single-wavelength Brillouin fiber laser (BFL) is demonstrated at the extended L-band region using bismuth-based erbium-doped fiber (Bi-EDF) for the first time to the best of our knowledge. A 2.15-m-long Bi-EDF is used to provide both nonlinear and linear gains to generate a stimulated Brillouin scattering (SBS) and to amplify the generated SBS, respectively. The BFL operates at 1613.93 nm, which is upshifted by 0.09 nm from the Brillouin pump with a peak power of 2 dBm and a side-mode suppression ratio of more than 22 dB. The generated BFL has a narrow linewidth and many potential applications, such as in optical communication and sensors.