We computationally investigate cascaded amplification in a three-level mid-infrared (IR) Pr(3+)-doped chalcogenide fiber amplifier. The overlap of the cross-sections in the transitions (3)H(6)→(3)H(5) and (3)H(5)→(3)H(4) enable both transitions to simultaneously amplify a single wavelength in the range between 4.25 μm and 4.55 μm. High gain and low noise are achieved simultaneously if the signal is at 4.5 μm. We show that 45% of pump power that is injected at 2 μm can be shifted to 4.5 μm. The efficiency of using a mid-IR fiber amplifier is higher than what can be achieved by using mid-IR supercontinuum generation, which has been estimated at 25%. This mid-IR fiber amplifier can be used in conjunction with quantum cascade lasers to obtain a tunable, high-power mid-IR source.