Semi-trailer trucks often face difficulty during manual parking owing to their complex structure and large blind areas. Thus, in order to resolve these issues, we propose a path planning and motion control method suitable for single-step perpendicular parking of semi-trailer trucks. In the planning stage, we consider the articulation angle as the maximum virtual steering angle of the semi-trailer truck to calculate its minimum turning radius. Then, we select a feasible starting point area by considering the collision constraint of the truck during the parking process and use the B-spline curve to plan a collision-free reference path. In the motion control stage, we consider the center of the rear axle of the semi-trailer truck as the research object so as to design a model predictive controller based on the established kinematic model. We then propose a reference information selection principle for the controller. Finally, we use Matlab and TruckSim to simulate and analyze different parking starting points and different parking space sizes. Our simulation results show that the parking starting point of the trailer is an arbitrary value in the feasible starting area and that the optional range of parking starting points can be expanded. Our proposed method enables the truck to be parked in a perpendicular parking space without collision and with less tracking error. This observation confirms the good control effect of the designed controller.