The conservative level-set method for capturing the interface between two fluids is combined with a variable density projection scheme to simulate incompressible two-phase flows on unstructured meshes. All equations are discretized by using a conservative finite-volume approximation on a collocated grid arrangement. A high order scheme based on a flux limiter formulation, is adopted for approximating the convective terms, while the diffusive fluxes are centrally differenced. Gradients are computed by the least-squares approach. Physical properties are assumed to vary smoothly in a narrow band around the interface to avoid numerical instabilities. The numerical method is validated against classical advection test and two-phase flow examples including topology changes. (C) 2014 Elsevier Ltd. All rights reserved.