Compared with the conventional horizontal conveyor-chain-type plastic-film-picking device, the longitudinal nail-tooth-chain-plate-type plastic-film-picking device developed by our team in the early stage has little tearing effect on the mulching film, and the separation effect of the plastic film and the impurity is better. With a view to further enhancing the performance of the plastic-film-picking device, this study optimized it and designed a friction-type nail-tooth-chain-plate plastic-film-picking chain that does not overload or slip and also facilitates the installation of functional components. The kinematic analysis of the picking nail teeth on the film-picking chain was carried out, and the motion equation and trajectory of the nail teeth during the operation were determined, as well as the requirements for the nail teeth to complete the mulching-film pickup. The key parameters of the plastic-film-picking system were determined by analyzing the no-leakage condition of the plastic film and the force. Moreover, the structural design and key parameters of the shovel-type film-lifting device were determined. According to the design results, a prototype was developed, and a multi-factor test of the operating parameters was carried out. The operating speed, spacing of the pickup nail teeth, depth of the film shovel into the soil, and distance between the tip of the film shovel and center of the picking drum were used as the experimental factors. The plastic-film pickup rate, impurity rate of the recovered mulching film, and traction resistance were used as the test indicators. A four-factor, five-level quadratic regression orthogonal combination experiment was conducted using the Central Composite Design (CCD). The effect of each test factor on the test index of the plastic-film-picking system was studied, the regression models were established, and the optimal parameter combination was acquired by using the multi-objective optimization method. When the working speed was 6 km/h, the pickup-nail-tooth spacing was 228.6 mm, the depth of the film-lifting shovel into the soil was 37 mm, and the distance between the tip of the film shovel and the center of the pickup drum was 130 mm, the field experiment shows that the plastic-film pickup rate was 90.12%, the impurity rate of the recovered mulching film was 8.96%, and the traction resistance was 19.905 kN. The relative errors between the test results and the predicted values of the regression models were less than 5%, indicating that the parameter optimization regression models were reliable, and the designed friction-type nail-tooth-chain-plate plastic-film-picking system met the technical requirements of agricultural-plastic-film recycling. The research results can provide a technical reference for the development of mulching-film collection machines.