Considering the Guassian distribution of the pump beam and the thermal effect in the gain medium, the coupled rate equations of a LD-pumped passively Q-switched Nd:YVO4 laser at 1.06 μm with Cr⁴⁺:YAG are given. The theoretical average output power, pulse width, and pulse repetition of the laser are obtained by the numerical solution of the rate equations. The experimental results accord with the numerical solutions of the coupled rate equations.