Abstract: This study is an investigation on upper bound for the chromatic number of a graph. In this study, it has been extended the concept of an upper bound for the chromatic number of a graph to total graphs. Further proved that the chromatic number, χ(T(G))≤[s/s+1(Δ(T(G)+2))] for any graph G where Δ(T(G)) is maximum degree in T(G), s be the maximum number of vertices with same degree.