Natural gas plays an important role in industry as a clean energy, with the intensification of the Russia-Ukraine war, there is a large-scale energy shortage in Europe, and the natural gas supply in Europe has a natural gas crisis due to the cut-off of the Nord Stream No.1 pipeline. Therefore, it is necessary to accurately predict the consumption of natural gas. In order to fulfill this requirement, this paper uses the Lagrangian Support Vector Regression model with Sorensen kernel based on the Nonlinear Auto-Regressive model and Grey Wolf Optimizer for 5-step forecasting of monthly natural gas consumption in all European countries. Under three time lags, comparing the 5-step predict results of GWO-LSVR with SVR, RF, LightGBM, XGBoost, and MLP, those five models’ hyperparameters also optimized by GWO, it found that GWO-LSVR has smallest MAPE in almost all cases, and the numerical results of MAPE generated by GWO-LSVR is from 5.844% to 11.622%, the smaller the forecasting step size, the better the effect. Moreover, compares the difference of GWO and WOA, it is found that GWO can obtained better model hyperparameters and smaller MAPE results. To sum up, the proposed GWO-LSVR model has strong generalization performance and robustness, and is a reliable natural gas consumption prediction model.