The single point upstream method, which is based on five point finite difference techniques, causes a problem of the grid orientation in predicting the recovery performance for severe condition like an unfavorable mobili-ty ratio, piston type displacement. The nine point method has been developed to reduce inaccuracy caused by the grid orientation. Although this method shows noticeable improvements over the orientation effects, it requires more computational time than the five point method. Therefore to increase the computing efficiency of reservoir simulation with keeping the same degree of accuracy, the five point method using three point upstream scheme is introuced in this study. To test the validity of the new method, the various confined five spot flood patterns such as unfavorable mobility ratio and piston type displacements have been employed. The results evaluated by three point upstream scheme are in the similar level of numerical accuracy, but take much less computational time than the nine point simulator.