In this paper, a walking algorithm of a biped robot with unknown dynamics has been addressed by proposing a new adaptive control based on the Modified Function Approximation Technique (MFAT) augmented with backstepping control, using state feedback and output feedback. The classical ZMP, the preview controller on the 3- Dimensional Linear Inverted Pendulum Model (3D-LIPM), is a stable walking algorithm but does not allow high accuracy, high speed, and robustness due to the ground environment, and also due to the dynamics uncertainties caused by the complex structure of these kinds of robots. To improve the accuracy of the walking tracking performance of the biped robot and its robustness against dynamics uncertainty and external perturbations, a combination of backstepping control and MFAT strategy have been intended. Recursive Lyapunov function is developed to ensure the closed-loop system stability. Experiment simulation and comparative study were carried out with biped robot to verify the performance and the robustness of the developed control strategy.