This paper proposes a novel algorithm for joint space position/torque hybrid control of a mammal-type quadruped robot. With this control algorithm, the robot demonstrated both dynamic locomotion and push reaction abilities without the need for torque control in the ab/ad joints. Based on the tipping and slipping condition of the legged robot, we showed that reaction to a typical push in the horizontal direction does not require full contact-force-control in the frontal plane. Furthermore, we showed that position/torque hybrid control in Cartesian space is directly applicable to joint space hybrid control due to the joint configuration of the quadruped robot. We conducted experiments on our legged robot platform to verify the performance of our hybrid control algorithm. With this approach, the robot displayed stability while walking and reacting to external push disturbances.