Soft robots can perform effectively inspecting than rigid robots in some special environments such as nuclear pipelines and high-voltage cables. This article presents a versatile quadruped soft rod-climbing robot (SR-CR) that consists of four bending actuators and a telescopic actuator. The bending actuator is composed of flexible bellows with multiple folding air chambers, elastic telescopic layer (ETL), and strain-limiting layer (SLL). The telescopic actuator provides the energy for the robot to climb forward. The SR-CR is activated by a control strategy that alternates the body deformation and feet pneumatic clenched for stable climbing. The robot can climb rods at 90°, with the maximum speed of up to 2.33 mm/s (0.018 body length/s). At 0.83 HZ, the maximum moving speed of the robot in climbing horizontally parallel rods can reach 18.43 mm/s. In addition, the SR-CR can also achieve multiple impressive functions, including turning around a corner at a rate of 7 mm/s (0.054 body length/s), carrying a payload of 3.7 times its self-weight on horizontal rods at a speed of 9 mm/s (0.069 body length/s).