A central pattern generator (CPG)-based controller enhances the adaptability of quadrupedal locomotion, for example, by controlling the trunk posture. The conventional CPG-based controllers with attitude control often utilized the posture angle as feedback information. However, if the robot’s body is as soft as a musculoskeletal structure, it can measure the over-tilting of the trunk based on proprioceptive information of the muscles. In general, proprioceptive information such as muscle tension changes more rapidly than posture angle information. Therefore, a feedback loop based on proprioceptive information has great potential to respond to sudden disturbances that occur during locomotion over uneven terrain. In this research, we proposed a CPG-based controller utilizing the tension of soft pneumatic artificial muscles (PAMs). Musculoskeletal quadruped robots driven by PAMs are so soft, which prevents over-extension of the leg and over-tilting of the trunk to some extent. In addition, tension, one of the proprioceptive information of PAMs, exhibits high sensitivity to changes in trunk posture because the soft body’s motion easily changes due to over-titing of the trunk. To validate the efficacy of the proposed controller, we conducted numerical simulations with a simple quadruped model and experiments with a musculoskeletal quadruped robot. As a result, the tension feedback was effective for posture stabilization when the robot’s locomotion was subjected to disturbances. Moreover, the tension feedback was effective in improving the running velocity over uneven terrain. These results will enhance the locomotion capability of musculoskeletal quadruped robots, advancing their practical application.