Aiming at the requirements of quadruped robots for mobile flexibility and stability, a quadruped robot single-leg flexibility control strategy based on the estimation of external force is carried out to realize the high-performance dynamic interaction of the robot’s position and force during the movement process. Firstly, the torque of the motor is modeled into a simpler form. The robot single-leg dynamics model is established, and the established dynamics model and current feedback value are used to estimate the change of the robot joint force during the action of the external force; finally, based on the estimated robot joint torque, the position-based impedance control is designed to make the robot foot end in flexible contact with the environment, and at the same time to ensure the accuracy of the robot foot end trajectory tracking. Simulation is carried out by Adams-Matlab/Simulink to verify the correctness of the theoretical model. The foot-end trajectory tracking experiments on a single leg going up a staircase are carried out to verify the validity of the single-leg supple-control method based on the estimation of the external force, which is widely applicable compared with the traditional active supple-control method because it does not require additional sensors, is inexpensive, and does not reduce the rigidity of the robot itself.