In order to reduce ground drop loss during mechanical pepper picking and improve the net recovery rate, a drum snap finger picking device was designed. The picking device is mainly composed of a picking drum and auxiliary picking components; the picking finger arrangement was designed biomimetically and its structure and operating parameters were optimized by the DEM (discrete element method). According to the physical and mechanical characteristics of the pepper and the simplified three-dimensional model of the picking device, a virtual simulation model of the pepper-picking device was established using the EDEM software. Through simulation analysis and using the orthogonal test method, the main factors which affect the ground drop loss rate of pepper and their optimal parameter combination values were determined. The simulation results were verified by a pepper-picking field experiment. Orthogonal tests show that, when the picking drum speed (V′) is 210 rpm, the pepper-feeding speed (V″) is 1100 mm·s−1, the bending angle of each picking spring tooth (C) is 162°, and each group of circumferential fingers has rows, the picking device has a good picking effect. At this time, the ground drop loss rates in both the simulation and field test were 7.50% and 7.85%, respectively, and the drop error was only 4.46%, which was within the allowable range. The design form and parameter optimization simulation method in this paper provide an important reference for the design and optimization of pepper-harvesting machinery.