We propose a coupled volume-of-fluid and level set (VOSET) method for interfacial flow simulations on unstructured triangular grids. In this method, the volume fraction advection is performed using a Lagrangian-Eulerian remapping algorithm, and the level set function is calculated by a simple iterative geometric operation. The present VOSET method can not only satisfy mass conservation but also predict the surface tension with good accuracy, thus combining the advantages and overcoming the disadvantages of volume-of-fluid (VOF) and level set (LS) methods. Finally, the present method is verified by well known Zalesak's slotted-disk revolution, single vortex flow, dam break and single bubble rising problems. The results illustrate that the present method can accurately simulate incompressible two-phase flows for unstructured triangular grids. (C) 2017 Elsevier Ltd. All rights reserved.