With the worldwide increasing concern regarding environmental protection and controlling carbon emission, carbon dioxide (CO2) displacement in the subsurface becomes a vital process in environmental engineering and petroleum engineering. In this study, we propose a new "D3Q27" three fluid phase lattice Boltzmann method (TPLBM) based on a multiple relaxation time algorithm to study the flow behavior of three fluids, water, CO2, and oil in this study. A series of TPLBM simulation studies are carried out on a three-dimensional digital replica of a rock (sandstone) to investigate the microprocesses and mechanisms of CO2 displacement from its oil-water-CO2 systems. Data gathered from high-resolution X-ray computed tomography scanning of a sandstone sample from Daqing oilfield, Longhupao, Songliao Basin, China, is used to construct the rock replica. TPLBM numerical simulations are conducted to analyze the microdisplacement of CO2 in sandstone under different injection conditions. The results show that the displacement efficiency is higher at higher injection rates and pressure differences, with a constant total volume of injected CO,. The optimal injection rate and pressure difference for CO2 displacement in sandstone are identified. The average ultimate CO2 displacement efficiency is 90.1% when the injection rate remains constant, whereas the average ultimate CO2 displacement efficiency is 95.8% when the injection pressure difference remains constant. The proposed method offers a new method for analyzing the pore-scale three fluid phase flow in sandstone.