A numerical solution of an annular two-phase flow in a square channel is presented. A combined formulation using only one set of conservation equations to treat both fluids is employed. The level-set (LS) method is used to capture the interface between the fluids. To overcome a weakness in the level-set method, the localized mass correction (LMC) scheme of  is applied to ensure mass conservation. The finite-volume method is used to solve the governing equations. Results are presented for two fluids of identical and different properties with two different inlet interface shapes. These results are compared with that of the volume-of-fluid (VOF) method and good agreement is achieved.