The AC algorithm solves the power flow equations by iterations, which is computationally infeasible to the online security analysis of power systems. A fast load flow calculation method is proposed based on a convolutional neural network (CNN). As to the offline training stage, the proposed method extracts inputs (initial feature maps) based on the changes in operating conditions and topologies. In abundant training samples, the CNN and maps the nonlinear relationship between the extracted feature maps and the targeted load flow results. When it comes to the online applications, the proposed method directly calculates the feature map and delivers the load flow results based on the CNN trained offline. As is indicated in the N-2 load flow simulations of four typical IEEE systems, the generalization capability is guaranteed. Compared with the AC algorithm, the proposed method accelerates the power flow computation by eighty times. The accuracy is enhanced by nearly one order of magnitude, compared with that of the traditional artificial neural network (ANN).