The 1.3 μm laser source has a wide range of applications in the fields of sodium beacons, optical communication, image display and laser medicine. In the paper, we demonstrate a laser with an LD end-pumped Nd:YAG slab crystal hybrid cavity Innoslab structure. When the pump power is high, the thermal effect of the laser during oscillation has an impact on the stability of the resonant cavity and the quality of the beam. We demonstrate a finite element model of an Nd:YAG crystal by means of heat conduction theory and analyse the effect of the temperature distribution at the crystal end face and the pump spot width on the thermal effect of the crystal. Calculations show that the finer the pump spot, the more pronounced the thermal effect of the crystal. In the experiment, the Nd:YAG slab crystal was doped at a concentration of 1at%, and a mixing cavity is constructed with a concave spherical mirror of R1 = 1000 mm and a convex cylindrical mirror of R2 = 900 mm; the length of the cavity is 55 mm; a negative cylindrical lens of Rc = -100 mm is inserted in the cavity as a compensating mirror. Finally, the maximum output power in the resonant cavity without the compensating mirror was 46.9 W; with the addition of the compensating mirror the maximum output power was 40.5 W; the vertical beam quality was increased from 2.98 to 1.28.