The mass-conserving level-set (MCLS) method is a hybrid level-set (LS)/volume of fluid (VoF) based, interface capturing algorithm that combines the mass conserving properties of the VoF, with the benefits of having an explicit description of the interface of the LS method. The efficiency of the method is a result of the fact that the LS formulation allows evaluation of the VoF-field and VoF-fluxes without reconstruction of the interface in each cell. We present the extension of the MCLS method from its original formulation for Cartesian quadrilateral control volumes to triangular control volumes for optimal geometrical flexibility. The LS field is discretized using a second order discontinuous Galerkin method. After each time-step, a mass-conserving correction is imposed based on the simultaneously convected VoF field. This convection step is performed with a second-order Eulerian–Lagrangian approach, combined with a ‘clipping’ algorithm to project the advected field from the Lagrangian to the Eulerian grid. The MCLS method is shown to be accurately mass conserving and shows second order convergence for three different test cases.