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Accurate forecast of natural gas consumption is of significance for policy makers to formulate energy plans, save costs and improve energy structure. This study designs a novel three-parameter discrete direct grey model denoted as TDDGM, which overcomes existing modeling drawbacks about the accumulating generation for monotonous series. Moreover, the optimal initial condition of the proposed model is deduced by the ordinary least square method and the final recursive function is derived. Error checking method of TDDGM and five different numerical cases are introduced to verify the superiority and effectiveness of the new approach. The results show that TDDGM performs better than other several benchmark models in multiple tests. Finally, it is utilized to forecast China's natural gas consumption and the predicted results will maintain a steady upward trend, reaching 322.06 billion cubic meters in 2022. The research results have positive significance for enriching grey system theory and improving energy structure in China. [ABSTRACT FROM AUTHOR]