Numerical simulation for evolutionary history of an oil-and gas-bearing basin is to repeat geological and thermodynamic history of basin evolution on a computer and then to quantitate petroleum generation, accumulation and migration. The mathematical model describing geological and thermodynamic history of the basin evolution is characterised by an initial-boundary value problem of a system of nonlinear partial differential 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 a practical model is given, which shows that the abnormal pressure and paleo-temperature computed are reasonable and display physical characteristics clearly as well.