This paper constructs a two-sector environmental growth model with explicit mathematical derivation and economic intuition in a social planning economy. Through the optimal allocation of man-made capital between the production sector and the environmental sector, this paper shows that the trade-off between economic growth and environmental protection exists only when an economy deviates from its steady state. We also provide short-run transitions for both the whole economic system and individual control and state variables. In addition, technological progress in the production sector benefits economic growth rate while the improvement of technology in the environmental sector has only level effects on economic variables. This paper ends with a link between the theory and a hot empirical issue — the environmental Kuznets curve (EKC) hypothesis.