An all-fiber mid-infrared supercontinuum (MIR-SC) laser source with a power of over 2 W beyond 3.8 µm is demonstrated. The SC laser involves a silica-fiber-based SC laser as a pump source and a piece of fluoroindate (InF3) fiber as a nonlinear medium. The influence of pump pulse repetition rate on the SC characteristics is carefully studied. In the InF3 fiber, the pump pulse with spectral coverage of 1.9-2.6 µm is converted into MIR-SC with a broadest spectral coverage of 1.9-4.9 µm and a maximal average power of 11.8 W. Up to 2.18 W is measured in the spectral region beyond 3.8 µm, which, to the best of the authors' knowledge, demonstrates the record SC power in this waveband to date.