Q-switched Microchip laser emitting radiation at wavelength 1342 nm was designed and characteristic study of a passively Q-switched ( V3+:YAG) diode pumped solid state laser system is presented , An active laser part (Nd3+:YAG), and a saturable absorber (V3+:YAG, T0 = 97 %).The microchip resonator consists of dielectric mirrors directly deposited on the monolith Surfaces, the output coupler has reflecting 95% @ 1342 nm was placed on the V3+-doped part. Q-switched microchip laser was tested under pulsed laser diode, has been investigated the laser output parameters such as energy, peak power, and pulse width a comparison between theoretically calculated results and simulation results using a software which calculates the Q-switched solid state laser parameters was performed. There was a good agreement with the theoretical calculations and the simulation values.