YAG/Nd:YAG and YAG/Nd:YAG/YAG composite laser crystals were fabricated through thermal bonding method. The temperature distribution and laser properties of Nd:YAG, YAG/Nd:YAG and YAG/Nd:YAG/YAG crystals under LD end-pumping conditions were studied. Laser outputs with wavelengths of 1064 nm and 946 nm have been achieved. Temperature simulation results revealed that at 20 W pump power, the YAG/Nd:YAG/YAG crystal exhibited 15 K lower temperature compared to Nd:YAG crystal, with a 33 K reduction in end-face temperature. Under 20 W pumping, the maximum continuous-wave output powers of YAG/Nd:YAG/YAG crystal reached 4.412 W at 1064 nm and 668 mW at 946 nm, corresponding to slope efficiencies of 34.66 % and 6.68 %, and optical-to-optical conversion efficiencies of 34.77 % and 5.99 %, respectively. These values represent 1.6-fold and 1.8-fold improvements in output power, 13.4 % and 4.33 % enhancements in slope efficiency, as well as 9.31 % and 3.92 % increases in conversion efficiency compared to Nd:YAG crystal. Moreover, the YAG/Nd:YAG/YAG crystal demonstrated superior beam quality with lower M2 factors than both Nd:YAG/YAG composite crystal and Nd:YAG crystal. It is shown that the composite YAG/Nd:YAG/YAG crystal has better cooling efficiency, which is beneficial to reduce the thermal lens effect and improve the laser efficiency.