This paper presents a technique of motion planning of robot using Fuzzy Method and Genetic Algorithm along with Three Path concept in a dynamic environment which contains both static and dynamic obstacles. The algorithm is divided into two phases. In the first phase, a path or two is generated by using Three Path Method or Fuzzy-GA while considering static obstacles only. The information about the distances and angles of obstacles from the robot is acquired by using the concept of Three Path. A collision free path is selected by using Three Path concept. When all the three paths are blocked by static obstacles Fuzzy Method is used for obstacles avoidance. Genetic Algorithm is used to find optimal range of the linguistic values of the variables for the membership functions. In the second phase, the moving obstacles are avoided along the path/paths generated in the first phase by considering the velocities of the moving obstacles and the velocity of the robot. Results show that the technique of motion planning of mobile robots using Fuzzy-GA along with Three Path concept is computationally efficient as compared to other hybrid methods for motion planning in dynamic environment.