We present a detailed study of a combined actively and passively Q-switched (CAPQ) laser with an acousto-optic modulator (AOM) and a codoped Cr4+, Nd3+ :YAG crystal. The hybrid Q-switch approach is used to produce a short laser pulse with stable and tunable repetition rates. The timing jitter, average pulse width, and average pulse amplitude vary periodically with the AOM modulation frequency under a fixed pump power. The repetition rate of the CAPQ laser can be tued approximately from 4 kHz to 16 kHz with the jitter less than 400ns.