This paper introduces a numerical method for curvature calculation, termed least square-normal and curvature (LSNC), for simulating the migration of twodimensional boundaries. The method is based on the existing volume-of-fluid (VOF) method with new algorithms to calculate the normal and the curvature of a boundary. The LSNC method is applied to solve a number of simple problems pertaining to boundary migration driven by curvature and a uniform 'force' associated with an energy density difference across the boundary. The accuracy of the LSNC method is assessed by comparing its results with exact solutions, when available. The method proved more accurate than the Ripple method, which is described in the literature as another variant of VOF methods.