To improve its cleaning performance, the peanut sheller’s air–screen cleaning device was used as the research object, and a numerical simulation was carried out. A scheme was proposed to optimize the installation angle of the screen surface of the air–screen cleaning device, and the influence of the airflow velocity of the sieve surface before and after the structural improvement of the machine on the airflow distribution of the whole chamber was evaluated. At the same time, the computational fluid dynamics–discrete element method (CFD–DEM) of coupling simulation was used to carry out single-factor simulation tests on the improved air–screen cleaning device, analyze the movement trajectory, velocity, and displacement of the extrudates in the cleaning chamber, characterize the separation law of extrudates, and determine the parameter ranges for each factor. In addition, based on the central composite Box–Behnken design, an orthogonal simulation test was carried out with three factors, including fan speed, amplitude, and vibration frequency, and the influence of each factor on the kernel loss rate and impurity rate was investigated. Furthermore, the influencing factors were optimized, and the optimal parameter combination was obtained; when the fan speed was 1682.72 r/min, the amplitude was 3.74 mm, and the vibration frequency was 492.86 Hz, it was more conducive to the cleaning of kernels. Finally, the accuracy of the simulation and optimization methods was verified via the machine test, and the optimal parameter combination was obtained: at a fan speed of 1680 r/min, an amplitude of 3.7 mm and a vibration frequency of 490 Hz were achieved, and the kernel loss rate and impurity rate were 2.01% and 2.42%, 3.71 and 4.42 percentage points lower than those before optimization, respectively.