Abstract: This paper defines the adjacent cost matrix and the path matrix based on the directed weighted-graph, and defines a new operator that "summarization then minimum" replace "multiplication then summarization" between two adjacent cost matrixs, named "minimum of summarization sequence between two multiplication position elements of the two matrixs". Based on this new matrix operator, this paper proposes a new algorithm to the shortest path problem within a directed graph. This algorithm can get the global shortest path out for any types of graph. Dijkstra algorithm is a well-known good solution to the shortest path problem, but it will result out a fake path to some kinds of graph. The algorithm presented by this paper completely overcome this phenomena out of Dijikstra algorithm.