While technological revolution has active role to the increase of computer information, growing computational capabilities of devices, and raise the level of knowledge abilities, and skills. Increase developments in science and technology. In graph used the shortest path algorithms for solving the shortest path problem. The shortest path can be single pair shortest path problem or all pairs shortest path problem. This paper discuss briefly the shortest path algorithms such as Dijkstra's algorithm, Bellman-Ford algorithm,FloydWarshall algorithm, and johnson's algorithm. It describes the previous algorithms for solving the shortest path problem. The goal of this paper is to investigate and comparison the impacts of different shortest path algorithms. The study shows that the efficiency varies among algorithms, helps to suggest which one of them ought to be used to solve a specific variant of the shortest path problem.