The paper aims to propose a capping device based on the 2-PSR/UPU parallel mechanism to solve the capping process on the production line today, to solve the problem of the capping on the inclined surface of different inclination angles on the production line. The 2-PSR/UPU parallel mechanism model was established. The reverse position solution of the mechanism was solved according to the fixed length constraint condition, and the reverse position solution pose was verified by the corresponding motion example. By comparing the multiple reverse postures, the effective solution was solved; the workspace was solved by the three-dimensional coordinate search method. The workspace of the 10mm reference point below the moving platform of the parallel mechanism was continuous and free from voids, and could adapt to the screwing problem on the inclined surface of the 0-35° range, and the parallel mechanism was provided with an example of a capping in the case of 25°, 30°, and 35°. The capping device based on the 2-PSR/UPU parallel mechanism has a simple structure and adjustable mechanism, and can achieve precise control on the production line. The special function of 1-translation and 2-rotation of the parallel mechanism is adapted to the capping task of the inclined surface with different inclination angles.