In order to more accurately characterize the effects of nanoparticles on lubricant viscosity, the effects of copper dialkyl dithiophosphate (HDDP)-modified (CuDDP) nanoparticles on the dynamic viscosity of mineral oils 150N, alkylated naphthalene (AN5), diisooctyl sebacate (DIOS), and polyalphaolefins (PAO4, PAO6, PAO10, PAO40, and PAO100) were investigated at an experimental temperature of 40 °C and additive mass fraction ranging from 0.5% to 2.5%. CuDDP exhibits a viscosity-reducing effect on higher-viscosity base oils, such as PAO40 and PAO100, and a viscosity-increasing effect on lower-viscosity base oils, namely, 150N, AN5, DIOS, PAO4, PAO6, and PAO10. These effects can be attributed to the interfacial slip effect and the shear resistance of the nanoparticles. The experimental dynamic viscosity of the eight base oils containing CuDDP was compared with that calculated by the three classical formulae of nanofluid viscosity, The predicted viscosity values of the formulae deviated greatly from the experimental viscosity values, with the maximum deviation being 7.9%. On this basis, the interface slip effect was introduced into Einstein’s formula, the interface effect was quantified with the aniline point of the base oil, and a new equation was established to reflect the influence of CuDDP nanoparticles on lubricating oil viscosity. It can better reflect the influence of CuDDP on the viscosity of various base oils, and the deviation from the experimental data is less than 1.7%.