The most important thing for navigation of a mobile robot is to find the most suitable path and avoid the obstacles in the static and dynamic environment. This paper presents a method to search the optimal path in start space extended to time domain with considering a velocity and a direction of moving obstacles. A modified version of $A^*$ algorithm has been applied for path planning in this work and proposed a method of path search to avoid a collision with moving obstacle in space-tim domain with a velocity and an orientation of obstacles. The velocity and the direction for moving obstacle are assumed as linear form. The simulation result shows that a mobile robot navigates safely among moving obstacles of constant linear velocity. This work can be applied for not only a moving robot but also a legged humanoid robot and all fields where the path planning is required.