In this study, an interface-tracking method, NS-PFM, combining Navier-Stokes (NS) equations with a phase-field model (PFM) is applied to an incompressible two-phase free surface flow problem at a high density ratio equivalent to that of an air-water system, for examining the computational capability. Based on the Cahn-Hilliard free energy theory, PFM describes an interface as a finite volumetric zone across which physical properties vary steeply but continuously. Surface tension is defined as an excessive free energy per unit area induced by local density gradient. Consequently, PFM simplifies the interface-tracking procedure on a fixed spatial grid without any elaborating techniques in conventional numerical methods. It was confirmed through the numerical simulation that (1) the NS-PFM conducts self-organizing reconstruction of the interface with a certain thickness using volume flux driven by chemical potential gradient and (2) predicted collapse of two-dimensional liquid column in a gas under gravity agreed well with available data.