A picosecond mid-infrared optical parametric oscillator (OPO) synchronously pumped by an Yb-doped fiber laser is reported. The OPO is pumped by an all fiber master oscillator power amplifier (MOPA) centered at 1064 nm picosecond pulses with duration of 20 ps at a repetition rate of 52 MHz. A 50 mm periodically poled MgO-doped LiNbO3 (PPMgLN) with a poled grating period of 30.5 μm is used as the nonlinear crystal and a single resonant cavity is adopted. At room temperature, 0.67 W average idler is obtained at pump power of 5.2 W with the conversion efficiency from pump to idler being 12.9% and the slope efficiency being 14.5%. By controlling the temperature of PPMgLN crystal, the wavelength tuning range can cover 1.544~1.608 μm (singal) and 3.15~3.43 μm (idler). Additionally, the stability of this OPO system is discussed.