Finite difference frequency domain (FDFD) mode solvers are straightforward to implement but can suffer from slow convergence when applied to high-contrast refractive index structures. In this work, we show how subpixel smoothing can improve the convergence properties of a full-vectorial FDFD mode solver. Based on a standard Yee grid, we formulate a generalized eigenbproblem whose solutions provide the modes of the waveguides taking into account the tensor nature of the effective dielectric constant. We investigate the convergence of the proposed FDFD mode solver in several cases including a step index fiber, a microsctuctured fiber, and a cylindrical plasmonic waveguide. The results show that tensor smoothing can significantly improve the convergence of the solver, thus allowing the use of less dense grids in the calculations. Our implementation is freely available on the web under an open-source licence.