We demonstrate a 1.32 μm mode-locked bismuth fiber laser operating in both anomalous and normal dispersion regimes. In anomalous dispersion regime, achieved by using 13 nm/cm linearly chirped fiber Bragg grating, the laser exhibits multiple soliton operation with pulse duration of 2.51 ps. With the net normal cavity dispersion, the single-pulse operation with higher power has been obtained by avoiding the limitations generic to conservative soliton systems.