Natural gas is playing an important role in the reconstruction of the energy system of China. Natural gas supply and consumption indicators forecasting is an important decision-making support for the government and energy companies, which has attracted considerable interest from researchers in recent years. In order to deal with the more complex features of the natural gas datasets in China, a Grey Wavelet Support Vector Regressor is proposed in this work. This model integrates the primary framework of the grey system model with the kernel representation employed in the support vector regression model. Through a series of mathematical transformations, the parameter optimization problem can be solved using the sequential minimal optimization algorithm. The Grey Wolf Optimizer is used to optimize its hyperparameters with the nested cross-validation scheme, and a complete computational algorithm is built. The case studies are conducted with real-world datasets from 2003–2020 in China using the proposed model and 15 other models. The results show that the proposed model presents a significantly higher performance in out-of-sample forecasting than all the other models, indicating the high potential of the proposed model in forecasting the natural gas supply and consumption in China.