Abstract: Backstop technology makes energy substitution possible that it alleviates the scarcity of non-renewable energy constraints. By inducing nonrenewable and renewable resources in the Lucas's endogenous growth model, we focus on the relationship between the consumption of nonrenewable & renewable resources and economic growth in equilibrium growth path. Meanwhile, we investigate the necessary conditions for sustainable economic development and sustainable utilization of energy. Based on the results of this model，an econometric model is employed into empirical analysis of China. We conclude that the rate of human capital accumulation and renewable energy regeneration are the decisive factor in maintaining economic growth. Specifically, the rate of accumulation of human capital offsets the diminishing marginal effect of physical capital, and the reproducibility of renewable energy just makes up for the depletion of non-renewable energy constraints. So renewable resources is critical power in support of sustainable utilization of energy. Moreover, China's evidence implies that nonrenewable & renewable energy consumption significantly drive economic growth and that the former's contribution to economic growth is bigger than the latter's.