The number of users engaged in social media through social networks continues to grow as people become more passionate on current social issues and events. People using social networks tend to have different opinions or positions regarding these issues and events. However, social network users share similar characteristics such as political orientation, age, and gender. Since the users of social networks can be grouped according to their similarities, then we would like to observe how these users affect the belief and opinion of other users in the same or different groups. Inspired by this phenomenon, we propose a multi-population mean field game approach to capture the belief and opinion evolution of a social network with several populations. Through the proposed model, we can gain information on the behavior of social network users belonging to different groups. Moreover, we can utilize the proposed model to predict how social network users affect the belief and opinion of each other. The multi-population social network mean field game problem is solved analytically using an adjoint method. Then, simulations are provided to show the belief and opinion evolution of users in a multi-population social network.