Relative permeability measurement of decane-water two-phase flow was conducted in a fracture, created in granite, at confining pressures of 5 MPa and 10 MPa. Non-wetting phase (decane) relative permeability decreased with decreasing capillary pressure, indicating significant phase interference due to capillarity in two-phase flow through a rock fracture under confining pressure. Moreover, the relative permeability was much smaller at the same capillary pressure for the higher confining pressure, indicating that the phase interference became much more significant at a higher confining pressure. Consequently, the X model and the viscous coupling model, ignoring any phase interference and phase interference due to capillarity, respectively, were expected to be inappropriate for a fracture under confining pressure, emphasizing importance of evaluating two-phase fracture flow characteristics under confining pressure. However, it is difficult to measure phase saturation within a fracture under confining pressure. Consequently, a numerical non-steady-state two-phase fracture flow model, which considers influences of both viscosity and capillarity, was developed to determine a relative permeability-saturation-capillary pressure relation for the fracture aperture distribution under confining pressure. The model, which could be verified by experimental results, provided a non-wetting relative permeability curve, which was entirely different from the X model, the viscous coupling model, and even the Corey model. Moreover, an application of the model for air-water two-phase fracture flow provided a similar conclusion.