This paper describes a global path planning method and path optimization algorithm for autonomous mobile robot based on the virtual elastic force in a grid map environment. A goal of a path planning is information for a robot to go its goal point from start point by a effective way. The AStar algorithm is a well-known method for a grid based path planning. This paper suggest a path optimization method by a virtual elastic force and compare the algorithm with a orignal AStar method. The virtual elastic force makes a shorter and smoother path. It is a profitable algorithm to optimize a path in a grid environment.