In order to meet the demand of 13.5-nm extreme ultraviolet lithography (EUVL), an acousto-optically Q-switched CO₂ laser was developed, which has high repetition rate and high stability. First, the operating principle of the acousto-optic Q-switch was analyzed and the relationship between the voltage of modulated signal and diffraction efficiency was researched experimentally. And then, by studying the influence of modulated signal duty cycle on pulse waveform, the appropriate duty cycle was chosen to eliminate the pulse tail. Under the conditions of different repetition rates, pulse duration, power and the pulse amplitude stability were measured and analyzed. Finally, the beam pointing stability of the laser was measured. Experimental results indicate that the range of pulse repetition rate can be adjusted from 1 kHz to 100 kHz. When the repetition rate is 1 kHz, the minimum pulse duration is 252 ns and the maximum peak power reaches 7 579 W. By designing the support frames mainly made of invar steel, the unstablity of pulse amplitude is less than 3% and the beam pointing stability is only 46.6 μrad. This acousto-optic Q-switched CO₂ laser is suitable for a seed source used in EUVL.