In this paper, we present a parallel implementation of a solution for the Traveling Salesman Problem (TSP). TSP is the problem of finding the shortest path from point A to point B, given a set of points and passing through each point exactly once. Initially a sequential algorithm is fabricated from scratch and written in C language. The sequential algorithm is then converted into a parallel algorithm by integrating it with the Message Passing Interface (MPI) libraries so that it can be executed on a cluster computer. Our main aim by creating the parallel algorithm is to accelerate the execution time of solving TSP. Experimental results conducted on Beowulf cluster are presented to demonstrate the viability of our work as well as the efficiency of the parallel algorithm.