Navigation is a method to direct a mobile robot without collision when traversing the environment. This is to reach a destination without getting lost. In this paper, global and local path planning in fixed obstacle and moving obstacle using genetic algorithm are presented. First, mobile robot searches optimal global path using genetic algorithm without falling into local minima. Then if it finds a unknown obstacle, it searches new path without crashing obstacle. Also if there is a moving obstacle, mobile robot searches new optimal path without colliding with the obstacles. Various simulation results show the proposed algorithm can search a shortest path effectively.