In this study, a direct numerical simulation for analyzing the immiscible incompressible two-fluid flows was carried out with the 3-dimensional MARS method, and the applicability of this scheme was verified in the water column collapse phenomenon, 2-dimesional channel flows between two walls and 3-dimensinal air-water co-current flows between a non-slip wall and a free-slip wall. It was shown that the present numerical simulation was in good agreement with previous experimental and numerical results, and that the volume of fluid in flows was sufficiently conserved for the long simulation time step. However, it is pointed out in the 3-D air-water co-current flows that lack of simulation grids and inadequate averaged time generates the inaccurate results in this DNS.