As an important parameter to measure the leakage of electromagnetic energy through apertures, there has not been a universal, fast and high precision method to obtain the coupling cross section (CCS). For obtaining the hexagonal aperture array normalized CCS, we analyze the influence of various factors on it under the condition of vertical incidence. A total of 13820 sets of CCS data are obtained by selecting appropriate parameters and using full-wave analysis method. After some input parameters are preprocessed and the neural network is trained, a BP neural network model has been constructed with seven parameters including the electrical dimension of the aperture unit, row/column number, the electrical dimension of the row/column distance, the electrical dimension of the aperture wall thickness and polarization angle of incident wave as the input and the normalized CCS as the output. The model has an average relative error of 3.8% when the predicted normalized CCS of the hexagonal aperture array has the electrical dimensions [0.1, 1.2]. A total of 480 CCSs with input parameters not appearing in both the training set and the test set are predicted by the neural network and compared with the full-wave analysis results, and the average relative error is 7.27%. Finally, the universality and effectiveness of the model are validated further by experimental measurement.