Graph coloring problem is one of most frequent studied problem in the graph theory due to its uses in different area of applications like simulation of biological networks, communication networks, register allocation and many more. This problem involves the coloring of the vertices of the given a graph G (V, E) with number of available colors in such a manner that adjacent vertices must assign colors different with each other. In this paper we present a hybrid approach to assign the colors to vertices of the given graph that is based on adjacency matrix and search tree data structure. The coloring process for a particular vertex in the graph will done by getting the feasible colors available in the color list. The feasible colors that may be assigned to a vertex, retrieved from the vertex-color binary search tree generated initially for available colors. The proposed solution for the graph coloring problem is efficient in terms of its running time complexity and it will work without affecting its complexity for any kind of graph.