Thermal wavefront distortion in the gas cooled Nd:Glass laser amplifier based on edge heating is analyzed theoretically. Temperature distribution and thermal wavefront distortion under different heating temperatures of the Nd:Glass are simulated numerically and verified by an experiment. The results show that the numerical simulation is in good agreement with the experimental results. Thermal wavefront distortion decreases as the heating edge temperature increases when the heat deposition is 0.6 W/cm3, but starts increasing when the edge temperature is higher than 90 ℃. Optimal design of the edge heating structure and heating temperature can suppress the thermal wavefront distortion effectively in the gas cooled Nd:Glass laser amplifier.