In-pipe cleaning robots often need to carry cleaning tools, and their tails are connected with cables such as water pipes and air pipes. Especially when cleaning vertical straight pipes and curved pipes, a greater traction is required. Therefore, a new type of screw drive in-pipe cleaning robot was designed in this paper. The robot solves the problems of small traction, complex structure, and unstable motion of the in-pipe cleaning robot. The kinematics modeling was carried out on the screw drive in-pipe cleaning robot’s screw module for generating traction, and the force analysis was performed on this basis. The function model of the torque, air pressure, and traction of the screw module was established, which was verified by the simulation and experiment. The results show that the screw in-pipe cleaning robot has a large traction, stable operation, and can be well adapted to the vertical straight pipes and curved pipes.