As concerns about energy and environment emerge the concept of sustainable development, this paper develops a five-sector endogenous technological change economic growth model considering sustainable use of energy and pollution control. We introduce energy and environment into production function and utility function, solve the conditions for sustainable economic growth with the optimal control method, further reveal the dynamic relationship which should be met by energy consumption rate, pollution control and sustainable economic growth, prove the possibility of sustainable economic growth and reveal the path and conditions of sustainable economic growth under the dual constraints of energy and environment.