Based on the method of energy equipartition and thermal conduction equations and the thermal-elastic equations, a numerical model of the gradient dopant concentrations rod laser medium end-pumped by laser diode was set up. Considering the temperature correlation of the thermodynamic parameters of the material and heat transfer coefficient between air and medium, the distributions of absorption coefficient, absorption pump power, temperature, thermal stress and strain in the laser medium of constant doping, two stepwise gradient doping, five stepwise gradient doping and ideal gradient doping structures were calculated by a finite element analysis method. The results indicate that by using the gradient dopant concentrations laser medium, absorption pump power uniformity in laser medium can be improved greatly. And the maximum temperature and principal tensile stress and principal strain of the five stepwise gradient doping laser medium were respectively 42.6% and 31.9% and 28.1% of the constant doping laser medium. It is obvious that the thermal effects of the gradient dopant concentrations laser medium are greatly reduced. The theoretical results provide theoretical reference and experimental study for the design of solid laser pumped by laser diode.