The gain saturation of Nd-glass amplifier is determined by the relaxation rate of populations. The influences of the thermalization rates among the components of the multiplets to which the laser levels belong and of the depletion rate of terminal laser level are investigated in detail. A modified Frantz-Nodvik model in consideration of the influence of thermalization and depletion between laser levels is obtained. By solving these differential equations, we calculated a practical amplifier. The results indicate that the output of the amplifier can increase remarkably when the thermalization time decreases to pulse duration.