A new numerical method is developed for the robust simulation of high-Reynolds number two-fluid flows with high density contrast. The proposed method is a combination of the consistent mass–momentum transport framework of Nangia et al. (2019) [5] and the coupled level-set and volume-of-fluid method of Sussman and Puckett (2000) [23]. The conservative form of the momentum equation is solved, and the convection equation of density is solved together with the momentum equation at all cell faces. Moreover, consistent spatial and temporal discretization schemes are used to advance the governing equations of density and momentum to ensure a stable simulation. In the proposed method, the diffusion of the density or viscosity around the interface is not needed. In the test of a canonical case, the convection of a high density droplet, the proposed method makes an accurate prediction of the interface dynamics with a relatively low grid resolution. This feature is useful for reducing the computational cost for two-fluid flows with complex interface geometries. Furthermore, the test results show that the simulation is also stable for high Reynolds number two-fluid flows. In the case of wave breaking, the proposed method is stable for a high Reynolds number of ��=108. In the test case of a collapsing and impinging water column, the present method makes good predictions on the water height and pressure that agree well with experimental results.