We numerically show that when a gas filled hollow-core photonic crystal fiber is pumped by two-color pulses, an ultra-short pulse can be generated in the mid-infrared. This phenomenon is due to the cascaded nonlinear phenomenon starting from a spectral broadening of the two pulses combined with an induced phase-matched four wave-mixing lying in the midinfrared, with a dispersive wave. By selecting the mid-infrared band with a bandpass filter, we demonstrate the generation of 60 fs pulses at 3-4 µm and an ultra-short pulse duration of 20 fs can be reached with additional phase compensator.