The study tested how the wavelet transform of the data affects the accuracy of an artificial neural network model for forecasting surface methane concentration. A model based on the nonlinear autoregressive neural network with external input (NARX) was used. For comparison, we used the base NARX model and the hybrid model. The hybrid model was created based on the data to which the discrete wavelet transform (DWT) was applied. For DWT, the Daubechies wavelet of the fourth level was used. The initial data for the study were collected on the measurements of the concentration of greenhouse gases in the Russian Arctic zone. We evaluated the accuracy of the models by the following indicators: Mean absolute error, root mean square error, and the index of agreement. The proposed approach has improved the accuracy of the forecast. The accuracy of the hybrid model has increased by more than 10%.