A passively Q-switched solid state monolithic laser based on the composite Nd∶YAG/Cr∶YAG crystal is studied. A Cr∶YAG saturable absorber is taken as the passively Q-switched unit and the component integration design is adopted. A laser with output energy of 3.5 mJ, pulse width of 2.1 ns and peak power of 1.67 MW is obtained. The performance factors reach the same level in the world. The key parameters of this monolithic laser are calculated based on the passively Q-switched rate equation, and the theoretical pulse energy value is basically consistent with the experimental value. A prototype of the Nd∶YAG/Cr∶YAG monolithic laser is obtained based on the integration and assembly of the components of a composite monolithic laser, which can successfully breakdown the air near the target and induce plasma. The preliminary requirement as a laser plug is satisfied.