Narrow pulse laser can be obtained from laser diode (LD) pumped acousto-optically (A-O) Q-switched all solid state lasers (SSLs), which is useful in many applications such as laser ranging, laser radar, etc. According to Q-switching rate equation, the relationships between pulse average power, pulse width and inverted population density are explained by theoretical analysis and reasonable model. LD side pumped Nd:YVO4 crystal which is polarized absorption and emission in a flat-flat cavity is used to achieve narrower pulse width. On conditions that the pumped current is 32.6 A, the repetition rate is 33.5 kHz, the cavity length is 62 mm, the transmittance is 50%, the shortest pulse width of 4.4 ns is obtained. On conditions that the pumped current is 31.6 A, the cavity length is 77 mm, a 1064 nm laser output with the pulse width of 5.5 ns and the peak power of 26 kW is obtained. Cavity length, repetition rate and transmittance of output mirror as functions of pulse width have been discussed.