This paper addresses the shortest path problem in time-dependent networks, where links can be negative. This kind of shortest path problems has a wide variety of applications such as transportation and logistics management. We propose a new solution algorithm which is modified from Dijkstra’s algorithm and include both negative links and time-dependency. The importance of this algorithm is that it can solve these specific shortest path problems easily because of consideration of these two limitations. The performance of this new approach was tested on an example network.