In this study, design of a novel robust control method for three-link underactuated biped robot which can satisfy appropriate constrains on the robot and cause the stability and rhythmic movement of the robot, is presented. Due to the wide use of sensors and actuators in mechanisms and robots, and existence of noise and also uncertainty in the system components or other error stemming from unmolded dynamics in the system or unwanted disturbances acting on them, there is an essential need for employment of robust control methods. In order to apply locomotion’s constrains to the system, the feedback linearization method is used. Additionally this method is combined with the sliding mode method to obtain a robust control method. The other purpose of the study is the complete elimination of chattering phenomenon. To this end, the control method is combined with the backstepping method. Finally, the exponential stability of the method, which is called FLBS, is proved, and the stability of the obtained walking cycle is shown using the Poincare map. In the robot modeling procedure, the contact between the swing leg and the ground is considered to be rigid and instantaneous. The underactuated nature of the robot and the importance of the role of contact in stabilizing the robot movement are taken into account in this study. Finally, simulations based on this control method are performed which show the exponential stability of robot movement, elimination of chattering and robustness against either disturbances or uncertainties.