Index trend prediction is a critical topic in the sphere of financial investment. An index trend prediction model based on a multi-graph convolutional neural network termed MG-Conv is suggested in this paper. First, the data normalization and one-dimensional convolutional neural network are proposed to extract the deep features of historical transaction data. Then, two types of correlation graphs named static and dynamic graphs are defined. Finally, the multi-graph convolution is performed on these two graphs, and the results of graph convolution are transferred to anticipated values with fully connected networks. 42 Chinese stock market indices were selected as experimental data. Classic approaches including LSTM , 3D-CNN, GC-CNN, and AD-GAT were chosen as comparison benchmarks. The results show that the method can reduce the average prediction error by 5.11% and performs strong robustness. • Combining transaction data from multiple indices improves forecasting. • Graph based on constituent stocks can better reflect correlations of indices. • Graph convolution that fuses static and dynamic graphs improves prediction. • Multi-graph convolutional index trend prediction reduces model overfitting.