Foam flooding can improve the development effect by increasing the flow resistance. The conventional models for calculating flow resistance are mostly based on empirical formulas. The process of foam formation and stabilization cannot be characterized in empirical formula. In this paper, the online nuclear magnetic resonance visualization experimental system was used. We conducted experiments on the influence of different experimental conditions on flow resistance. Combined with the fractional flow model, a new resistance factor model with multiple undetermined coefficients is established. By fitting the experimental results, the undetermined coefficients were determined, and a program for calculating the seepage law of one-dimensional gas water two-phase foam flooding was developed. The experimental results show that the flow resistance of foam is directly related to the starting pressure water saturation and critical water saturation. There is a quantitative relationship between the rising pressure water saturation, critical water saturation, gas water ratio, permeability, and displacement rate. A new flow resistance model that can characterize the theory of foam formation and collapse is established. On this basis, the foam flooding flow calculation program can calculate one-dimensional core pressure, gas and water saturation and other parameters change. Compared with the results of online nuclear magnetic resonance experiments, the fitting accuracy can reach 96%. The new model realizes the accurate calculation of the evolution mechanism of foam and the plugging effect of foam in the seepage process of foam.