Soft robots have unique advantages over traditional rigid robots and have broad application prospects in many fields, such as pipe inspections. Several of the reported pipe-crawling soft robots have long actuation periods and small locomotion speeds. Moreover, they lack active steering property to adapt to complex piping systems, such as T-shaped pipes. To solve the above problems, this paper proposes a novel parallel-pipe-crawling pneumatic soft robot consisting of three extensible pneumatic soft actuators and two flexible feet. The parallel structure and flexible feet allow the robot to reduce the number of steps in a crawling cycle. The extensible actuator allows the robot to change its body shape for active steering property. However, a complete mathematical model for soft robots with parallel structure is hard to establish. In this paper, the phenomenological modeling method is used to realize a mathematical model with high precision, limited calculation, and easy engineering applicability of the pipe-crawling soft robot. Then, the prototype of the robot is fabricated with the optimal structural parameters selected by finite element simulations. The static identification experiment shows that the average errors of the extended length and output force are 0.51 mm and 0.28 N, respectively. The crawling experiments in various scenarios show that the horizontal crawling speed is higher than 15 mm/s, the maximum load is 2.456 kg, and the minimum turning radius is 38.2 mm. The robot shows great potential for inspecting in complex pipes with high crawling efficiency, excellent flexibility, and strong adaptability by switching its crawling gaits. INDEX TERMS Finite element simulation, parallel, phenomenological modeling, pipe-crawling robot, soft robot.