This paper investigates on the relationship between energy demand and income growth. Our hypothesis is that the logistic energy demand and durable goods demand basically result from bell-shaped income distribution. Income growth does not proportionally or linearly affect nergy demand along the income growth path. This paper has developed a simple model in which income distribution plays a role in determining energy demand growth path. It shows that the same level of income growth has a different effect on energy demands. The sensitivity of energy demand depends on the level of avarage per capita income and the shape of income distribution. This paper also shows that if income variance is smaller, the faster the sensitivity reaches its peak and the diminishing speed of sensitivity is also fast.