Abstract: Quadruped robots have the potential to traverse challenging natural environments with payloads. Recent advancements have demonstrated the efficacy of optimization-based control methods for locomotion of quadruped robots; however, these methods rely heavily on precise dynamic models to meet high performance. When robots carry unknown payloads, the resulting payload-induced dynamic uncertainties can significantly degrade performance or even lead to failure in practical applications. To address this issue, a motion control method integrating quadratic programming (QP) with adaptive control techniques is proposed. First, an adaptive parameter estimator based on Lyapunov stability analysis is designed to achieve online identification of the unknown payload mass. Subsequently, a nonlinear disturbance observer (DOB) is introduced to provide real-time compensation for torque disturbances caused by payload variations. Building upon this foundation, a QP-based balance controller is developed to solve optimal foot contact force allocation under friction cone constraints. Finally, simulations and real-world experiments under various payloads and operating conditions are conducted on the Unitree Go1 quadruped robot. Experimental results demonstrate that the proposed method outperforms comparison methods in terms of centroid trajectory tracking accuracy and body posture stability, verifying its effectiveness and robustness.