In view of the low prediction accuracy of ResNet, a method of DenseResNet (DRNet) for approximation of autonomous systems and series prediction is proposed based on the relationship between observed data and the system phase trajectory. Firstly, in order to strengthen the extraction and the circulation of ‘feature information’ contained in the data, all the outputs of previous layers in each hidden layer of feedforward neural network are concatenated as an input of this layer to form a dense block. Secondly, to avoid the ‘degradation’ phenomenon occurs when the depth of neural network increases, the residual mechanism is introduced to connect the input layer and output layer of the dense block to form the DRNet. Finally, DRNet is applied to the linear model, Damped single degree of freedom system and nonlinear models, SEIRS model and Logistic Volterra model. The results show that DRNet outperforms the ResNet, Back Propagation Neural Network (BPNN) and DenseNet in terms of model approximation and prediction accuracy on both datasets of 5 000 and 10 000. According to the four evaluation indexes on the nonlinear models, DRNet has high effectiveness on autonomous systems. The DRNet also shows good noise immunity for its better performance on the data with 5% noise.