Iran as a developing country possesses rich and extensive energy resources, an advantage in energy-intensive industries. In different economic thoughts, the more important factors that influence economic growth include labor and capital. In this research, we investigate the Granger-Causality relationship between marginal energy consumption in residential and commercial sectors (as marginal demand of energy), in industry, transportation and agriculture sectors (as intermediate demand for energy) and Iranian economic growth in (1967-2004), using standard Granger-Causality test, Auto Regressive with Distributed Lags and error correction models. The results of standard Granger-causality test reveal that there is unidirectional Granger Causality from marginal demand of energy to economic growth, and a bidirectional between intermediate demand of energy and economic growth. Estimation of error correction models reveals that in the short run and long run, there is bidirectional Granger-Causality between marginal demand of energy and economic growth as well as between intermediate demand of energy and economic growth.