The common shortest path problem is to find the shortest route between two specified nodes in a transportation network with only one traffic mode. The public transportation network with multiple traffic mode is a more realistic representation of the transportation system in the real world, but it is difficult for the conventional shortest path algorithms to deal with. The genetic algorithm (GA) is applied to solve this problem. The objective function is to minimize the sum of total service time and total transfer time. The individual description, the coding rule and the genetic operators are proposed for this problem.