The invention discloses a training method and system of a deep neural network based on critical damping momentum. The method comprises the following steps: S1, starting a new round of iteration; S2, inputting a batch of new images, and calculating traces of a Hessel matrix of a loss function of the neural network, the Hessel matrix being a matrix formed by second derivatives of the loss function to each parameter of the neural network; S3, substituting the trace of the Hessel matrix into a critical damping solution of a second-order differential equation, and calculating to obtain a momentum coefficient of a neural network weight parameter; S4, updating parameters of the neural network in cooperation with a learning rate attenuation strategy; S5, judging whether all image batches are calculated or not, and if so, executing the step S6; if not, returning to the step S2; and S6, judging whether the iteration turns reach the maximum or not, if so, ending the training, and if not, returning to the step S1. According to the method, a stochastic gradient descent method containing momentum is improved, and an ideal training effect is achieved.