A sigma coloring of a non-trivial connected graph G is a coloring c : V (G) → N such that (u) 6= (v) for every two adjacent vertices u, v ∈ V (G), where (v) is the sum of the colors of the vertices in the open neighborhood N(v) of v ∈ V (G). The minimum number of colors required in a sigma coloring of a graph G is called the sigma chromatic number of G, denoted (G). A coloring c : V (G) → {1, 2, · · · , k} is said to be a magic sigma coloring of G if the sum of colors of all the vertices in the open neighborhood of each vertex of G is the same. In this paper, we study some of the properties of magic sigma coloring of a graph. Further, we define the magic sigma chromatic number of a graph and determine it for some known families of graphs.