Aiming at the problems of complex model and difficult calculation of ultra-short pulse fiber amplifier, a pulse evolution prediction method based on deep learning of gated recurrent unit was proposed. The gate recurrent unit model was trained respectively based on the initial pulse information in the time domain and frequency domain. One nonlinear pulse compression process in thulium-doped fiber amplifier is successfully predicted, which matched the numerical calculation and experimental results. Compared with solving the nonlinear Schrödinger equation and the rate equation, this method has higher operation speed, which is beneficial to optimize the amplifier parameters and understand the nonlinear dynamic process of ultra-short pulses in the gain fiber.