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The single-source shortest path problem (SSSP), known as the basis of many application areas, is a fundamental matter in graph theory. In this paper, a new efficient algorithm named Li-Qi (LQ) is proposed for SSSP to find a simple path of minimum total weights from a designated source vertex to each vertex. The algorithm is based on the ideas of the queue and the relaxation, The main differences between this strategy with the Breadth-first search and the Bellman-Ford algorithm are that the vertices may be queued more than once and only the source vertex and relaxed vertices are queued; the algorithm terminates when the queue is empty. Experimental evaluation on different sizes of the generated graphs validates that the proposed algorithm far outperforms the simplest implementation of the DijkstraÂ¿s algorithm and surpasses the Bellman-Ford algorithm by about 2 times.