A novel hydrocyclone including a cylindrical screen embedded in a conventional hydrocyclone (CH), named three products hydrocyclone screen (TPHS), has been successfully designed. In TPHS, the combination of centrifugal classification and screening was employed to separate particles. In this paper, Grey theory, as an effective means to the laws of both complex and uncertainty system’s behavior with small samples, was used to investigate the operational (feed concentration and feed pressure) and structural (aperture size, spigot diameter, and vortex finder diameter) parameters on performance evaluation Hancock classification efficiency (HE), imperfection (I), and cut size (d50c). The experiments of coal sample (0−1 mm) show that TPHS with coarser particles in underflow exhibited the absent “fish-hook”. The closeness calculated using the Grey System algorithm indicates that the performance of TPHS was closely related to the operation and structure parameters. Further, the order of grey incidence degree between different parameters and HE (or I or d50c) is the spigot diameter and aperture size with the highest value, the feed pressure and vortex finder diameter with the middle value, and the feed concentration with the lowest value. The prediction using the GM(1, N) algorithm implies that the dynamic prediction model for the performance evaluation can be created depending on the operation, structure and previous performance value. The mean relative errors between the predicted and actual HE, I, and d50 were 2.84%, 5.83%, and 3.57%, respectively, which exhibit the accurate prediction.