In recent years, CO2 has been utilized to be injected into natural and induced fracture reservoirs with the purpose of enhanced natural energy resources recovery. In this study, the influence of liquid and supercritical CO2 properties under different pressure and temperature conditions on flow behaviors through a 3D self-affine fracture with rough surfaces is investigated with the application of Lattice Boltzmann method (LBM). CO2 has properties highly dependent on pressure and temperature and this study focuses on the liquid and supercritical CO2 properties because it is very common for CO2 to maintain liquid and supercritical states in deep reservoirs. LBM was used to simulate liquid and supercritical CO2 flow through a single fracture with rough surfaces. In addition to CO2 properties, the effects of pressure differences between the injecting and discharging surfaces of the fracture were also considered. The density and dynamic viscosity of CO2 display similar trends in responses to changes in pressure and temperature. Simulation results show that the average velocity of CO2 flow changes considerably with temperatures and pressures. The streamlines distributions revealed the changes of tortuosity under different temperature and pressure conditions, which follows a similar trend to that of the average velocity. A detailed analysis of the effects of the temperature, pressure and upscaling velocity on tortuosity was conducted based on the relevant curves and streamlines distributions. It was found that the values of tortuosity have a close relationship with the kinematic viscosity, which depends on temperature and pressure conditions.