Navigation and obstacle avoidance problems are introduced and solved in this paper. A new algorithm called quadratic Bezier curves is used to navigate a mobile robot in an unknown environment. The quadratic Bezier curve can be improved through a division and conquer technique whose basic operation is the generation of multiple midpoints on a specific curve. The platform of the mobile robot is constructed with three ultrasonic sensors placed around the front of the platform with 45° between them. These sensors are utilized to sense the locations of obstacles in any environment surrounding the mobile robot. Based on sensor(s) detection for obstacles in the environment of the mobile robot, five different scenarios are introduced and studied. To navigate the robot in the unknown environment, two main points are taken into consideration: Firstly, the smooth rotation of the mobile robot around the obstacles should be performed to avoid a collision; and secondly, the shortest path should be followed by the robot to reach a target with minimum time. Visual basic language is used to simulate the navigation of mobile robot in different environments. The quadratic Bezier curves algorithm is investigated real-time experiment, and the obtained results have proved the efficiency and evaluation of the proposed algorithm.