This paper is based on dynamic optimization methodology to investigate the economic energy efficiency issues in developing countries. The paper introduces some definitions about energy efficiency both in economics and physics, and establishes a quantitative way for measuring the economic energy efficiency. The linkage between economic energy efficiency, energy consumption and other macroeconomic variables is demonstrated primarily. Using the methodology of dynamic optimization, a maximum problem of economic energy efficiency over time, which is subjected to the extended Solow growth model and instantaneous investment rate, is modelled. In this model, the energy consumption is set as a control variable and the capital is regarded as a state variable. The analytic solutions can be derived and the diagrammatic analysis provides saddle-point equilibrium. A numerical simulation based on China is also presented; meanwhile, the optimal paths of investment and energy consumption can be drawn. The dynamic optimization encourages governments in developing countries to pursue higher economic energy efficiency by controlling the energy consumption and regulating the investment state as it can conserve energy without influencing the achievement of steady state in terms of Solow model. If that, a sustainable development will be achieved.