We report a novel quasi-synchronously pumped PPMgLN-based high power mid-infrared (MIR) laser with picosecond pulse bunch output. The pump laser is a linearly polarized MOPA structured all fiberized Yb fiber laser with picosecond pulse bunch output. The output from a mode-locked seed fiber laser was directed to pass through a FBG reflector via a circulator to narrow the pulse duration from 800 ps to less than 50 ps and the spectral FWHM from 9 nm to 0.15 nm. The narrowed pulses were further directed to pass through a novel pulse multiplier through which each pulse was made to become a pulse bunch composing of 13 sub-pulses with pulse to pulse time interval of 1.26 ns. The pulses were then amplified via two stage Yb fiber amplifiers to obtain a linearly polarized high average power output up to 85 W, which were then directed to pass through an isolator and to pump a PPMgLN-based optical parametric oscillator via quasi-synchronization pump scheme for ps pulse bunch MIR output. High MIR output with average power up to 4 W was obtained at 3.45 micron showing the feasibility of such pump scheme for ps pulse bunch MIR output.