We report the design of an ultrashort pulse amplifier based on using a chalcogenide gain fiber with a praseodymium doped core for operating in the 4–5 μm range on the (3F2, 3H6 ) → 3H5 and 3H5→3H4 transitions. A detailed numerical simulation with allowance for dispersive and nonlinear effects for two pumping schemes: four-level at 1.55 μm and three-level at 2 μm with different fiber optical losses, pulse repetition rates, and central signal wavelengths is presented. The preferable case is cascade amplification on both laser transitions with overlapping emission cross sections for seeding pulses at 4.3 μm pumped at 1.55 μm. In this case, a gain of more than 30 dB can be achieved. The pulse energy can be increased from 10 pJ up to >10 nJ for the repetition rate of order 1 MHz even for the loss level of 3 dB/m. The produced ps pulses have broadband spectra with Fourier transform limitation of order 100 fs. Further amplification may be limited by fiber damage.