The mid-infrared femtosecond optical parametric amplifier (OPA) in silicon waveguide is proposed and investigated numerically. Through appropriately engineering the waveguide dimensions, the zero-dispersion wavelength of the silicon waveguide can be tailored to 2.1μm and the broadband phase-matching can be realized. We achieve a conversion efficiency of −40dB and a conversion bandwidth of over 300nm for a low pump peak power in 8-mm-long silicon waveguide. We also analyze the evolution of the pump, signal and idler pulses in the process of optical parametric amplification. The proposed OPA exhibits compact configuration and can find important applications in integrated broadband optical source and ultrafast all-optical signal processing in mid-infrared.