An interface-capturing method for simulating two-phase flows in complex geometries is proposed. A structured orthogonal grid is used, and the presence of stationary solid boundaries is taken into account by using the volume fraction of the solid phase in a computational cell. The transport equation of the fluid volume fraction in the presence of solid boundaries is derived. The fluid phases are transported by using the THAINC (tangent of hyperbola with adaptive slope for interface capturing) method. An immersed boundary method is implemented to accurately calculate the volume flux of each fluid phase through a computational cell face, a part of which is blocked by the solid phase. Transportation of a fluid square in the presence of solid boundaries is carried out, to con firm that the errors in shape and volume conservation are low. The applicability of the proposed method to two-phase flows in complex geometries is examined through simulations of a flow about cylindrical tubes in a staggered arrangement and a dam break problem with an obstacle. In the former the pressure drop in the single-phase condition agrees well with the available correlation and the gas-liquid behavior in the tube geometry is qualitatively well predicted. The predicted liquid flow in the dam break problem also agrees well with available experimental data.