In this paper, a bismuth-based erbium-doped fiber amplifier (Bi-EDFA) that operates in both the C- and L-band wavelength regions is demonstrated. The system employs two pieces of bismuth-based erbium-doped fiber (Bi-EDF) as the gain medium with a midway broadband fiber Bragg grating (FBG). The FBG functions to prevent the gain saturation at the C-band region, flatten the overall gain spectrum, and reduce the noise figure, particularly for the C-band. At an input signal power of $-$30 dBm and a pump power of 150 mW for both pumps, a flat gain of around 29 dB is obtained with a gain variation of $pm$3.5 dB within the wavelength region from 1525 to 1615 nm using a backward-pumping scheme. At an input power of 0 dBm, the gain varies from 10 to 13 dB within the wavelength range from 1530 to 1620 nm, while the corresponding noise figure varies from 9.5 to 14 dB over this wavelength range.