The injection of fuel-generated CO₂ into oil reservoirs will lead to two benefits in both enhanced oil recovery (EOR) and the reduction in atmospheric emission of CO₂. To get an insight into CO₂ miscible flooding performance in oil reservoirs, a multi-compositional non-isothermal CO₂ miscible flooding mathematical model is developed. The convection and diffusion of CO₂-hydrocarbon mixtures in multiphase fluids in reservoirs, mass transfer between CO₂ and crude, and formation damages caused by asphaltene precipitation are fully considered in the model. The governing equations are discretized in space using the integral finite difference method. The Newton-Raphson iterative technique was used to solve the nonlinear equation systems of mass and energy conservation. A numerical simulator, in which regular grids and irregular grids are optional, was developed for predicting CO₂ miscible flooding processes. Two examples of one-dimensional (1D) regular and three-dimensional (3D) rectangle and polygonal grids are designed to demonstrate the functions of the simulator. Experimental data validate the developed simulator by comparison with 1D simulation results. The applications of the simulator indicate that it is feasible for predicting CO₂ flooding in oil reservoirs for EOR.