Due to the complexity of the engineering system and the uncertainty of the parameters，the dynamic control equations established by the principles of mechanics are often difficult to meet the requirements of precision. This paper studies data-driven system modeling and response prediction. First，the numerical solution of the dynamic state equation is used to simulate the system response under different external excitations measured in the experiment，and the neural network model is trained with the response data. The loss function containing the known relationship between the training data is constructed to improve the accuracy of the neural network，and the data model expressing state relationship is obtained. Then，the neural network model is incorporated into the ordinary differential equation solver to predict the response of the system under different excitations and obtain the amplitude frequency response relationship. The modeling method is applied to the spring mass system with cubic and gap nonlinearity respectively. The calculation results show that an accurate data model can be established based on the response data and the hysteresis and jump responses of the nonlinear system at the main resonance can be obtained. The study also shows that the more the training data has and the more complete the data is，the better the accuracy of the data model and the smaller the error of the predicted response will be.