In this paper, we proposed a finite element model of composite crystals to solve the thermal effect of disk crystal end-pumped by LD. The model was established based on the heat conduction theory, which is related to the working characteristics of continuous LD end-pumped YAG/Yb∶YAG disk. The effects of different factors such as the pump power, composite crystal thickness, and cross section size on the temperature field were analyzed by setting LD pumping parameters. The results showed that when the geometry of the composite crystal is constant, the temperature of the crystal increased with increasing pump power. At 70 W pump power, the pump spot radius was 400 μm via the collimation focusing of the optical coupling system, the thickness of Yb∶YAG crystal was 3 mm, and the thickness bonding of YAG crystal changed from 0 mm to 0.7 mm. Furthermore, the rise in maximum radial and axial temperatures decreased by 39.7 ℃ and 238.3 ℃, respectively. Under the same pumping conditions and with a 0.5 mm thick YAG crystal, the cross section radius of composite crystal increased from 8 mm to 13 mm, the maximum temperature rise along the radial and axial directions decreased by 32.8 ℃ and 171.7 ℃, respectively. Thus, the composite crystals can reduce the thermal effect inside laser crystals, which is significant for realizing high-power outputs of solid-state Yb∶YAG lasers.