The cylinder liner surface finish, which is commonly produced using the honing technique, is an essential factor of engine performance. The characteristics of the texture features, including the cross-hatch angle, the plateau roughness and the groove depth, significantly affect the performance of the ring pack–cylinder liner system. However, due to the influence of the honed texture features, the surface roughness of the liner is not subject to Gaussian distribution. To simulate the mixed lubrication performance of the ring–liner system with non-Gaussian roughness, the combination of a two-scale homogenization technique and a deterministic asperities contact method is adopted. In this study, a one-dimensional homogenized mixed lubrication model is established to study the influence of groove parameters on the load-carrying capacity and the frictional performance of the piston ring–liner system. The ring profile, plateau roughness, and operating conditions are taken into consideration. The main findings are that for nonflat ring, shallow and wide groove textures are beneficial for friction reduction, and there exists an optimum groove density that makes the friction minimum; for flat ring, wide and sparse grooves help improving the tribological performance, and there exists an optimum groove depth that makes the friction minimum.