We report on infrared supercontinuum (SC) generation in step-index fluoroindate-based fiber by using an all-fiber laser source. In comparison to widely used ZBLAN fibers for high-power mid-infrared (MIR) SC generation, fluoroindate fibers have multiphoton absorption edges at significantly longer wavelengths and can sustain similar intensities. Recent developments highlighted in the present study allowed the production of fluoroindate fibers with MIR background loss of 2 dB/km, which is similar to or even better than ZBLAN fibers. By using an all-fiber picosecond laser source based on an erbium amplifier followed by a thulium power amplifier, we demonstrate the generation of 1.0 W infrared SC spanning over 2.25 octaves from 1 μm to 5 μm. The generated MIR SC also exhibits high spectral flatness with a 6 dB spectral bandwidth from 1.91 μm to 4.77 μm and an average power two orders of magnitude greater than in previous demonstrations with a similar spectral distribution.