In view of the problem that peanut harvesting in hilly areas mainly involves fresh food, and that the peanut-picking purity rate is low and there is high breakage in the peanut-harvesting process, key components such as the picking system of a fresh-peanut-picking crawler combine harvester, the picking tooth, and the concave screen were designed, and ANSYS Workbench 2020 software was used to check the reliability of the picking roller under working conditions in hilly areas. In the process of equipment operation, the picking purity rate and breakage rate were the main evaluation indexes, and the Box–Behnken test method was used to study the speed of the peanut-picking roller, the feeding amount, and the picking gap as the test factors. The results showed that the picking purity rate is 98.95%, with an error margin of 0.98%, compared to the predicted value under the conditions of 342 r/min speed, 0.75 kg/s feeding amount, and 32 mm picking gap. The breakage rate is 4.23% and the error is 0.4% compared with the predicted value, indicating that the optimized model is reliable and predictive. This study provides a theoretical basis for the optimal design of the peanut-picking system of peanut-picking combine harvesters in hilly areas.