A picosecond fiber laser system based on master oscillator power amplifier (MOPA) is proposed. A passive mode-locked fiber laser with a semiconductor saturable absorber mirror (SESAM) which is with repetition rate of 29.87 MHz is used as the seed source. The repetition rate can be reduced to 574 kHz when a pre-amplifier system is combined with an acousto-optic modulator (AOM). The MOPA structure is based on rod-type photonic crystal fiber (PCF). The pulse with pulse width of 30 ps can be amplified based on properties of large mode field and high gain of PCF, and the spectral expanding caused by the self-phase modulation is effectively suppressed. Results show that the spectral linewidth of 5 dB is proportional to the peak-power of optical pulse of the proposed system (the beam quality factor M2 is 1.01 at the output power of 20 W). The peak-power of the picosecond pulse is 3.4 MW, which is near the diffraction limit. The picosecond pulse with the highest average output power of 21.86 W, pulse width of 11.1 ps, center wavelength of 1030.74 nm and linewidth of 1.75 nm at 5 dB can be obtained.