This paper presents a posture stabilization algorithm that can respond to slope changes caused by irregular ground obstacles and to unexpected impacts during walking of a quadruped robot. For this purpose, we devised a strategy to generate vertical ground reaction forces and horizontal ground reaction forces on the feet of a quadruped walking robot using a cart-inverted pendulum model with double-input double-output (DIDO). This strategy was devised using a linear quadratic regulator (LQR); stabilizing moment and stabilizing force were generated to control the robot’s torso inclination and left and right movement. The method of changing the quadratic programming (QP) constraint conditions according to whether an individual foot was in contact with the ground during walking was used to generate appropriate ground reaction forces for the support feet. In addition, vertical speed control of the swing feet was performed in the swing-down phase so that robot was able to land softly on the ground. Finally, in an environment in which external impact disturbance and irregular ground disturbance were applied together, we verified the performance of the proposed algorithm using the GAZEBO simulation and compared performances between proposed algorithm and our previous inverted pendulum model-based algorithm.