Ants release a chemical called pheromone while searching for food. Ants are capable of finding shortest path to their target .Observing their behaviour an ACS (Ant Colony System) algorithm was proposed. Earlier ACS has been used to give solution for many problems like travelling salesman problem. We propose to use ACS to solve Multi-stage graphs. Ant colony system can effectively give optimal solution in Multi-stage graphs. This approach can be used in real world applications like Grid computing, Data Mining etc.