The classical Dijkstra’s algorithm to find the shortest path in graphs is not applicable to multigraphs. In this study the authors generalize the classical Dijkstra’s algorithm to make it applicable to directed multigraphs. The modified algorithm is called by Generalized Dijkstra’s algorithm or GD Algorithm (GDA in short). The GDA outputs the shortest paths and the corresponding min cost. It is claimed that GDA may play a major role in many application areas of computer science, communication, transportation systems, in particular in those networks which cannot be modeled into graphs but into multigraphs.