As the applications and the demands of in-pipe robot are increasing, the problems in robot such as the coupling of output functions, the low positioning accuracy and the low reliability in complex environment, are becoming more and more serious. The axiomatic design theory was applied to the design of in-pipe robot, and a purely hydraulic drive in-pipe robot based on the flexible support structure was presented, which can meet the special needs in the horizontal well. The principle and process of axiomatic design were summarized, and the robot concept design was carried out to complete the design coupling analysis. The concrete composition of mechanical system and hydraulic system of robot were designed and its working mechanism was analyzed. Based on AMESim, the motion principle of the robot was simulated and analyzed, and the results show that the robot can achieve automatic reciprocating motion, the traction force can reach 30 kN, and the motion speed can reach 0.12 m/s. Moreover, the traction capacity and the motion speed of the robot can be adjusted separately, which means the decoupling design is realized.