Autonomous mobile robots such as differential drive mobile robots really need an intelligent navigation system that is able to avoid collisions with any obstacle from the starting point to the destination point. These collisions can be avoided by planning a collision-free path first. This study uses a modified genetic algorithm method to planning collision-free paths with static obstacles. Modification of the genetic algorithm is carried out on the crossover process by making rules that the fitness value of the progeny should be compared with fitness value of the parents. The chromosome with the best fitness value will be taken and used for the mutation process. Meanwhile the chromosome with poor fitness value will be completely ignored. Several experiments were carried out to achieve the desired criterion such as shortest path and fast execution time. The simulation result shows that the modified crossover genetic algorithm is able to generate optimal solutions based on the desired criterion.