Recent modification of the J-function model for obtaining the average oil-bearing rock capillary pressure based on the Leverett J-function have not fundamentally improved this technique, and modifications based on the rock pore-network model remain challenging. Because of this, a new method based on filling in 3-D curvilinear surfaces was developed for obtaining the average capillary pressure. The accuracy of the new method was verified by comparing the calculated results with the experimental data, which are in agreement. These findings suggest that the new method can be used to obtain the accurate average capillary pressure.