In this paper, A Lyapunov-based control design for an eight-degree-of-freedom quadruped robot is presented. A controller is required to control the quadruped robot parameters and maintain its stability during the walking. A dynamic equation of the quadruped robot needs to be developed to design and implement the controller. Dynamic modeling of quadruped robots developed with the help of the Euler–Lagrange method. The equations obtained from the dynamic model of the quadruped robot are non-linear. A Lyapunov-based controller has been proposed for the convergence of the state trajectory of the non-linear dynamic equation of a quadruped robot. The performance of the designed controller is analyzed via MATLAB simulation and discussed.