We demonstrate a high-peak-power and narrow pulse mid-infrared (MIR) laser with xenon-lamp pumping and La₃Ga₅SiO₁₄ (LGS) Q-switching on the Cr,Er:YAP crystal grown by Czochralski method. X-ray powder diffraction and x-ray rocking curves suggest the crystal has high crystalline quality. Segregation coefficients of the Cr^{3 +} and Er^{3 +} in the as-grown Cr,Er:YAP crystal are 4.96 and 1.07, respectively. The absorption and fluorescence spectra indicate that the Cr,Er:YAP crystal is a promising material for MIR laser by xenon-lamp pumping. The fluorescence lifetimes of the upper (I_11/24) and lower (I_13/24) laser levels are 0.86 and 3.57 ms, respectively. A maximum energy of 632 mJ is acquired at 5 Hz by xenon lamp pumping. By the LGS electro-optic Q-switching technology, single pulse energy of 148.6 mJ is achieved at 5 Hz with a pulse width of 35.4 ns and peak power of 4.2 MW. The results show that the LGS Q-switched Cr,Er:YAP crystal pumped by xenon lamp possesses potential application as a short-pulse and high-energy laser device.