The laser with high repetition rate, high peak power and narrow line width has important application value in the field of laser radar. In the amplification of high repetition frequency and narrow line width laser, in order to achieve both high magnification and high beam quality laser output at high repetition rate, narrow line width of passively Q-switched laser used to be the seed source, high gain amplifier using 888 nm diode laser end pumped Nd:YVO4 crystal, side pumped Nd:YVO4 slab crystal thermal lens effect of two stage amplification scheme were designed. At the repetition rate of 10 kHz, the average power of 31.5 W, and the laser beam quality of M2 1.98 were obtained. The peak power was 5 MW, the line width was 154 pm and the pulse width was 0.6 ns. Thus, the design idea of amplifier with high magnification ratio and high beam quality control individually was verified.