A set of coupled rate equations for diode-pumped Q-switched and mode-locked laser with electro-optic (EO) modulator and middle semiconductor saturable absorber mirror under the Gaussian spatial distribution approximation are given. The numerically simulated results of these equations show that the pulse width of the Q-switched envelope are related to the repetition rate of EO, the stimulated emission section of the gain medium, the pump power and so on. When the pulse width of the Q-switched envelope is shorter than the cavity roundtrip transmit time, i.e., the interval of two neighboring mode-locking pulses, there is only one mode-locked pulse lying in a Q-switched envelope and its repetition rate depends on that of EO. This means that single mode-locking pulses with low repetition rate, subnanosecond duration, high peak power, and high stability are generated. The simulated results are consistent with the experimental values.