Abstract. We introduce a new computational technique for evolving interfaces, the flux-based level set method. A nonlinear degenerate advection-diffusion level set equation is discretized by a finite volume method using a complementary volume strategy. It enables to solve the problem in an efficient and stable way. Using a flux-based method of characteristics for the advective part and a semi-implicit treatment of diffusive part, it removes the standard CFL condition on time step and it decreases CPU times significantly. The method is presented for 2D and 3D interface motions driven in normal direction by a constant and spatially varying driving force and (mean) curvature. Comparisons with known exact solutions and further numerical experiments, including topological changes of the interface, are presented.