A laser master oscillator power amplifier (MOPA) system consisting of a fiber amplifier and a two-stage Yb:YAG single crystal fiber (SCF) is experimentally studied. The nonlinear stimulated Raman scattering (SRS) is avoided by limiting the output power of the fiber preamplifier to 600 mW. Due to the benefit from the low nonlinearity and high amplification gain of the SCF, a laser pulse duration of 16.95 ps and a high average power of 41.7 W at a repetition rate of 250 kHz are obtained by using a two-stage polarization controlled double-pass amplification of Yb:YAG SCF, corresponding to an output energy of 166.8 J and a peak power of 9.84 MW, respectively. The polarization controlled SCF amplification scheme achieved a gain as high as more than 69 times. During the amplification, the spectra gain narrowing effect and the polarization controlled four-pass amplification setup are also studied. The laser spectrum is narrowed from over 10 nm to less than 3 nm, and the pulse width is also compressed to hundreds of femtosecond by dechirping the laser pulse. This compact-sized, cost-effective laser source can be used in laser micromachining, or as the seeder source for generating much higher power and energy laser for scientific research. For some applications which need femtosecond laser, this laser source can also be compressed to femtosecond regime.