This project proposes the convolutional neural network by using connectomes. The diagnosis of brain tumor types generally depends on the clinical experience of doctors, and computer-assisted diagnosis improves the accuracy of diagnosing tumor types. Therefore, a convolutional neural network based on complex networks (CNNBCN) with a modified activation function for the magnetic resonance imaging classification of brain tumors is presented. The network structure is not manually designed and optimized, but is generated by randomly generated graph algorithms. These randomly generated graphs are mapped into a computable neural network by a network generator. The accuracy of the modified CNNBCN model for brain tumor classification reaches 95.49%, which is higher than several models presented by other works. In addition, the test loss of brain tumor classification of the modified CNNBCN model is lower than those of the ResNet, DenseNet and Mobile Net models in the experiments. The modified CNNBCN model not only achieves satisfactory results in brain tumor image classification, but also enriches the methodology of neural network design. This project is implemented with MATLAB software.