Hermite-Gaussian (HG) beam mode decomposition has important applications in quantum communications and super-resolution imaging. The traditional convolutional neural network based on deep learning can realize mode decomposition of light field intensity and phase based on a single intensity image of HG beams, and the system is simple. In this study, the mode decomposition and reconstruction of a Hermite-Gaussian intensity diagram based on the new network architecture of Swin Transformer are investigated. In an experiment, the superimposed light fields of six modes (where the weights and phases are random values) of HG₀₀, HG₁₀, HG₀₁, HG₂₀, HG₁₁, and HG₀₂ are used as the output light fields. Experimental results show that when six eigenmodes are involved, the weight prediction error of the scheme is 0.05 and the phase is 0.15. In reconstructing the intensity image using the predicted weights and phases, we find that the input intensity image is very similar to the predicted intensity image. This work is of certain significance for large-capacity quantum communications, spatial quantum measurements, and super-resolution imaging.