A high average power passively Q-switched LD side-pumped laser system at 1 064 nm was set up by using Nd∶YAG/Cr∶YAG/YAG composite crystal. With 85% initial transmission of Cr∶YAG, the average output power of 1 064 nm was measured. Under the maximum pump power of 187.5 W, the maximum average output power of 83.68 W at 1 064 nm was obtained. By frequency doubling the 1 064 nm laser output in a KTP nonlinear crystal, 27.2 W green laser pulses at 532 nm with the corresponding pulse width of 210 ns and the repetition rate of 21.2 kHz were produced under the maximum pump power. The green laser single-pulse energy was 1.28 mJ and the peak power was 6.1 kW. And the optical-to-optical conversion efficiency of pump light to frequency-doubling light was 14.5%.