A proper coloring of the graph assigns colors to the vertices, edges, or both so that proximal elements are assigned distinct colors. Concepts and questions of graph coloring arise naturally from practical problems and have found applications in many areas, including Information Theory and most notably Theoretical Computer Science. A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least one vertex in each other color class. The b-chromatic number of a graph G, denoted by φ(G), is the maximal integer k such that G may have a b-coloring with k colors. In this paper, the authors find the b-chromatic number of middle and total graph of fan graph.