Inspired by musculoskeletal systems in nature, this paper presents a pneumatically actuated quadruped robot which utilizes two soft–rigid hybrid rotary joints in each of the four two-degrees of freedom (DoF) planar legs. We first introduce the mechanical design of the rotary joint and the integrated quadruped robot with minimized onboard electronic components. Based on the unique design of the rotary joint, a joint-level PID-based controller was adopted to control the angular displacement of the hip and knee joints of the quadruped robot. Typical gait patterns for legged locomotion, including the walking and trotting gaits, were investigated and designed. Proof-of-concept prototypes of the rotary joint and the quadruped robot were built and tested. The experimental results demonstrated that the rotary joint generated a maximum torque of 5.83 Nm and the quadruped robot was capable of locomotion, achieving a trotting gait of 187.5 mm/s with a frequency of 1.25 Hz and a walking gait of 12.8 mm/s with a gait cycle of 7.84 s. This study reveals that, compared to soft-legged robots, the quadruped robot has a simplified analytical model for motion control, size scalability and high movement speeds, thereby exhibiting significant potential for applications in extreme environments.