Lubricating oils are used in moving parts to minimize friction. The use of Nanofluids can enhance the properties of lubricants. The aim of this work is an enhancement of the rheology properties of base oil. The surface modification was conducted for inorganic nanoparticles (NPs) TiO₂-Al₂O₃ with oleic acid (OA) in this research. The OA renders the TiO₂-Al₂O₃ surface hydro-phobic. The OA-treated NPs show very stable dispersion in lubricating oil even after more than one month, compared with the unmodified NPs. The surface modification of NPs was characterized by Fourier transform infrared spectroscopy (FTIR). In this research, treated TiO2-Al₂O₃ are added to raw Iraqi lubricating oil 40 stock as a hybrid Nanofluid to study the rheology properties such as kinematic viscosity, viscosity index, and the stability of nano-fluid. Four different concentrations were prepared with a range of 0.2% to 1% by weight. Pour points and flashpoint was also identified. The TiO₂-Al₂O₃ nano lubricant shows a significant improvement in the viscosity index by 5.3–9.1 %, while the flashpoint increased by 5.8 – 14.36 % comparing with base oil.