The problems which are NP-complete in nature are always attracting the computer scientists to develop some heuristic algorithms, generating optimal solution in time-space efficient manner compared to the existing ones. Coloring of the vertices of a graph with minimum number of colours belongs to the same category, where the algorithm designers are trying to propose some new algorithms for better result. Here, we have designed modified Simulated Annealing (MSA) for optimal vertex coloring of a simple, symmetric and connected graph (GCP). The algorithm has been tested upon a series of benchmarks including large scale test case and has shown better output than the simple or non-modified version of the same algorithm. This paper describes the advancement of performance of simple SA applied upon the problem of graph coloring using a specially designed operator called random change operator instead of the general change operator. Our work is still going on for designing better algorithms generating optimal solutions. © 2012 Published by Elsevier Ltd.