Abstract: Numerical simulation for evolutionary history of an oil-and gas-bearing basin is to repeat geological and thermodyanomic history of basin evolution on a computer and then to quantitatc petroleum generation,accumulation and migration.The mathemat-ical model describing geological and thermodynamic history of the basin evolution ischaracterised by an initial-boundary value problem of a system of nonlinear partial dif-ferential equations.In the present paper,a numerical method for three-dimensional problem and the analysis of its stability are established and a numerical result for apractical model is given,which shows that the abnormal pressure and paleo-temperat-ure computed are reasonable and display physical characteristics clearly as well.