In this paper, we develop a new control method that brings together the advantages of fuzzy logic and sliding mode control. First, we introduce a non-chattering robust sliding mode control. Then, in order to improve the performance of the controller a fuzzy logic algorithm is integrated with the sliding mode controller. This algorithm decides the slope of the sliding surface of the sliding mode controller dynamically. Thus, the system is caught on the sliding surface rapidly and remains over it, more successfully improving the performance of the controller. Afterwards, to test the success of the controller introduced, it is applied to a planar robot, which is to follow a certain trajectory only using the control inputs produced. The results are compared with those of a conventional PID controlled system and a sliding mode controller with constant surface slope. In order to check the robust behavior of the controller designed, an unexpected change in the mass of the second link is introduced and to make the conditions tougher it is assumed that this change is not sensed by the controllers. Noise resistance of the proposed controller is also checked by introducing normally distributed noise components into the equations of motion of the robot model.