This paper proposes a new path-planning algorithm which is close to the family of bug algorithms. Path planning is one of the challenging problems in the area of service robotics. In practical applications, traditional methods have some limitations with respect to cost, efficiency, security, flexibility, portability, etc. Our proposed algorithm offers a computationally inexpensive goal-oriented strategy by following a smooth and short trajectory. The paper also presents comparisons with other algorithms. In addition, the paper also presents a test bed which is created to test the algorithm. We have used a two-wheeled differential drive robot for the navigation and only a single camera is used as a feedback sensor. Using an extended Kalman filter, we localize the robot efficiently in the map. Furthermore, we compare the actual path, predicted path and planned path to check the effectiveness of the control system.