Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX;posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX A compact pulsed Nd:LuAG laser at 1064 nm based on the self-Q-switching technique is reported, having the output power as high as 6.61 W at the incident pump power of 21.32 W, corresponding to the optical conversion efficiency of~31 %. The temporal width of the pulse was in the range from 532.2 ns to 652.6 ns, and the repetition rate varied between 488.6 kHz and 551.9 kHz. To the best of our knowledge, this is the first report on the self-Q-switching Nd:LuAG laser. Possible reasons for the self-Q-switching of Nd:LuAG were also provided, and the factor leading to the high repetition rate was analyzed. The compact cavity generating pulses with high output power and high repetition rate not only reveal that the self-Q-switching technique could be an efficient method for the generation of pulses with high output power and high repetition rate, but enrich the characteristics of Nd:LuAG crystal.