The research on 5G communication technology and the construction of new infrastructure has witnessed the rapid development of the smart grid. In the era of big data, the Internet of everything leads to the access of massive equipment to the power network, which also brings a great burden to the smart grid, and the stability problem of the power network is urgent to be solved. Therefore, we propose a prediction algorithm for smart grid stability based on Convolutional Neural Network (CNN). It collects the data generated by the power network, processes them in the CNN model, and finally outputs the judgment results of smart grid stability. The simulation results show that the algorithm has higher accuracy than SVM, AdaBoost, and random forest. Furthermore, four different optimization algorithms are used to improve the CNN model. SGD algorithm with momentum can achieve a prediction accuracy of 98.13%. The proposed model can effectively help the power system to pre-warn the unknown problems, reducing the security risks and power accidents.