In this paper, the effects of vibration parameters of a banana screen, i.e. frequency, amplitude and vibration direction angle, on the screening efficiency per unit time were studied using the discrete element method (DEM). The simulations were validated according to data collected from an experimental prototype screen. Functional relationships between vibration parameters and screening efficiency per unit time are presented. The results showed that the screening efficiency per unit time first displays an increase and later a decrease when the frequency, amplitude or vibration direction angle increased respectively. Vibration parameter optimization was also investigated, using an orthogonal experiment. Based on the banana screen model, it can be concluded that when the frequency is 22 Hz, the amplitude is 2.2 mm and the vibration direction angle is 39°, the screening efficiency of a banana screen is optimal.