Energy is an essential foundation for the economic growth and social development of a country. Since the reform and opening up, the economy in China has been in a state of rapid development and the paradox of the energy supply-demand has become increasingly prominent. An improved Grey-Markov chain model based on the wavelet transform is presented in this paper which takes various energy forms into account. The model uses the discrete wavelet transform for denoising, substitutes the extended grey model to the traditional one and introduces the fuzzy theory and metabolic principle into the Markov chain. Then an empirical example of China's energy production and consumption data during the period of 1990–2014 were selected as the research objects. Comparing with other methods, the proposed model was proved feasible and valid, and the energy production and consumption situation from 2015 to 2020 was predicted. Besides, the trend of energy supply and demand gap was analyzed as well as the energy structure which utilized the Shannon Wiener index. The results show that in the foreseeable future, the energy supply and demand gap in China will narrow and the energy structure tends to be diversified. Finally some opinions and suggestions are put forward. •Extended grey model is utilized to replace the traditional GM (1,1).•Fuzzy theory and metabolic principle are introduced to optimize the Markov chain.•Trend of China's energy supply and demand gap from 1990 to 2020 was analyzed.•Shannon Wiener index is used to study the energy structure.•Energy gap narrows and energy structure tends to be diversified in the future.