Robot navigation guides a robot moving from a start position to a target position without collision in an unknown environment. This paper proposes a robot navigation approach in a dynamic environment with static and dynamic obstacles. The proposed navigation method comprises static navigation and dynamic path planning (DPP). Static navigation guides the robot to avoid static obstacles by using a fuzzy controller, which comprises four input and two output variables. If the robot detects dynamic obstacles, a trajectory prediction table is generated to predict their moving trajectories. If this table shows that the robot will collide with a dynamic obstacle in the near future, DPP begins determining a safe and short path to avoid the obstacle by using the waiting or detouring strategies. The detouring strategy employs the A* algorithm to determine an optimal adaptable path to avoid a threatening obstacle. If the robot detects only static obstacles, the fuzzy controller guides the robot to avoid them. Simulation and comparison results showed that the proposed method is superior to static navigation.