Recent interest in complex systems and specially social networks has catalyzed the development of numerous models to help understand these networks. A number of models have been proposed recently where they are either variants of the small-world model, the preferential attachment model or both. Three fundamental properties attributed to identify these complex networks are high clustering coefficient, small average path length and the vertex connectivity following power-law distribution. Different models have been presented to generate networks having all these properties. In this paper, we focus on social networks and another important characteristic of these networks, which is the presence of Community Structures. Often misinterpret with the metric called clustering coefficient, we first show that the presence of Community Structures is indeed different from having high clustering coefficient. We then define a new network generation model which exhibits all the fundamental properties of complex networks along with the presence of Community Structures.