In order to research the applied advantages of composite crystals to the passively Q-switched lasers, a compact diode-end-pumped passively Q-switched laser was built up with a Yb∶YAG/Cr4+∶YAG/YAG composite crystal for generating efficient 1 030 nm and 515 nm pulsed lasers. The effects of pump power and initial transmission T0 on the laser properties were studied. As a result, a 1 030 nm laser with an average power of 1.97 W is obtained at T0 of 95% with slope efficiency of 33%, and the pulse peak power reaches to 87 kW at T0 of 85% with pulse width of 3.14 ns. In addition, in the frequency-doubled experiment with LBO, a green laser with higher output power of 634 mW is obtained at T0 of 90% with slope efficiency of 11.2% and pulse width of 15 ns. Finally, the red shift of spectrum and the leakage of output mirror were studied, as well as the method for increasing output power of green laser.