The differences of physical properties of water and air are the source of instabilities of the numerical solutions considering the free surface flow. The most typical methods for the free surface such as Volume Of Fluid(VOF) and Level-Set(LS) methods impose transient zones where the physical prosperities vary gradually for the stabilities of solutions. The thickness of the transient zone is the source of the error of a solution. The marker-density method does not use such a transient zone. In the traditional marker-density method, however, the air velocities of free surface cells are extrapolated from the water velocity and the pressures on the free surface are extrapolated form the air pressures for the stability of a solution. Those extrapolations are also the source of the error of the solution. In this study, the marker-density method is modified to calculate the air velocities of free surface cells by determining the pressure and velocity on the free surface to get continuous pressure gradient and viscous stress. Two-dimensional steady spilling breakers behind of a submersed hydrofoil is simulated using INHAWAVE-II including the modified marker-density(MMD) method. The results are compared with the results of Fluent V6.3 including VOF method and published research results. Moreover, three-dimensional spilling breaker near a wedge shaped ship model is simulated using INHAWAVE-II. And the results are compared with the results of Fluent V6.3 and exist experimental data.