This paper presents a coupled volume-of-fluid and level set (VOSET) method for unstructured triangular meshes to simulate incompressible two phase flows. In the method, a multi-dimensional advection algorithm, which includes 11 different cases for computing volume fluxes across cell faces, is proposed for the evolution of the volume fraction. An iterative geometric operation is presented to calculate the level set function. Thus, both advantages of volume-of-fluid (VOF) and level set (LS) methods are preserved in this unstructured VOSET method. Finally, the feasibility and accuracy of the current method are validated by three classical test cases -static drop, dam break, Rayleigh-Taylor instability problems. The current simulation results show good agreement with the experimental and numerical results in the literature. (C) 2017 Elsevier Ltd. All rights reserved.