The oil storage effect of textures is beneficial for lubrication performance under starved lubrication. When the larger of the two surfaces in friction pairs is textured, the moving textures should be considered because the boundary conditions are transiently changed at each moment. This is especially for the cross-hatched textures, which are manufactured on the cylinder liner while not on the piston ring. However, it means that the calculation cost will be very expensive for engineering friction pairs because the required calculation scale is very large and the required time step is very small. So the dynamic characteristics of moving textures on engineering surfaces are normally neglected in the existing researches. In this study, a starved lubrication model of the piston ring-cylinder liner (PRCL) system is established considering the oil storage effect, local hydrodynamic effect and dynamic characteristics of the moving cross-hatched textures. To speed up the calculation, an efficient parallel algorithm is developed. The results show that there is a significant difference in minimum oil film thickness (MOFT), wear load and oil film boundaries between stationary textures and moving textures, so the moving textures should not be simplified. This is helpful to find a better design of textures for engineering friction pairs.