We show that ultra-short pulses can be generated in the mid-infrared when a gas filled hollow-core fiber is pumped by a fundamental pulse and its second harmonic. The generation process originates from cascaded nonlinear phenomenon starting from a spectral broadening of the two pulses followed by an induced phase-matched four wave-mixing lying in the mid-infrared combined with a dispersive wave. By selecting this mid-infrared band with a spectral filter, we demonstrate the generation of ultra-short 60 fs pulses at 3-4 µm band and a pulse duration of 20 fs can be reached with additional phase compensator.