This paper presents a new strategy for path planning of a mobile robot by using a Genetic Algorithm. When a mobile robot moves from a point to another point, it is necessary to plan a optimal path avoiding obstructions in its way and minimizing a cost. On the other hand, Genetic Algorithms are search algorithms based on the mechanics of natural selection and natural genetics.They combine survival of the fittest among string structures with a structured yet randomized information exchange to form a search algorithm with some of the innovative flair of human search. An occasional new part is tried for good measure avoiding local minima. While randomized, Genetic Algorithms are no simple random walk. They efficiently exploit historical information to speculate on new search points with expected improved performance. For optimization, we apply the Genetic Algorithm to path planning of a mobile robot. We evaluate the proposed approach comparing with other optimization algorithms, such as Random Search and Simulated Annealing.