In most of the shortest path problems like vehicle routing problems and network routing problems, we only need an efficient path between two points—source and destination, and it is not necessary to calculate the shortest path from source to all other nodes. Dijkstra algorithm is called “ Single Source Shortest Path “.This paper introduces the Dijkstra algorithm in detail, and illustrates the method of implementation of the algorithm and the disadvantages of the algorithm .this algorithm applied on Directed weighted graph to find shortest path between two nodes ,but all weights in the graph should be non negative. In this paper we also discuss about how we can improve this algorithm in terms of finding path according to cost by increasing some no. of nodes.