Laser diode pumped solid state laser (DPSSL) has many applications. The thermal effect of laser crystal produced by pumping light is one of the main factors affecting the characteristics of DPSSL. Usually, the temperature field distribution in laser crystal is found first, then the thermal distortion of laser crystal is calculated by integrating thermal strain along crystal. This process is complex and difficult. Under the condition that the side surface of laser crystal has constant temperature and its ends are adiabatic, the heat conduction equation and integrating thermal strain are combined, the differential equation and boundary conditions of laser crystal thermal distortion are set. The ordinarily used two-step method is simplified to one step and the new differential equation can be solved much more easily than the old one. The analytical solution of thermal distortion differential equation of laser crystal with circular cross-section has been got. A computation example is also given. By numerical calculating, the relations between thermal distortion and curvature radius of distorted pumped-end of crystal with pumping beam radius are analyzed. The proposed simplified method for thermal distortion of end-pumped laser crystal has some generalization.