Autonomous navigation in dynamic environment heavily depends on the environment and its topology. Prior knowledge of the environment is not usually accurate as the environment keeps evolving in time. Since robot is continuously evaluating the environment as it proceeds, deciding the optimal way to traverse the environment to get to the goal, computationally efficient yet mathematically adaptive navigation algorithms are needed. In this paper, a navigation scheme for mobile robot, capable of dealing with time variant environment is proposed. This approach consists of a global planner (A*) and local planner (VFH) to assure an optimal and collision-free robot motion. The algorithm is tested both in simulation and experimentation in different environments that are known to result in failures in VFH and ROS navigation stack, for comparison purposes. Overall, the algorithm enables the robot to get to the goal faster and also produces a smoother path while doing so.