During the last years, multilevel methods have been applied in parallel circuit simulation. However, aiding the convergence of multilevel methods has gained only a little notice. This paper presents a combined Newton-Raphson and Gauss-Newton (NRGN) multilevel method for parallel circuit simulation in a networked environment. The NRGN method is formulated such that convergence aiding methods can be effectively applied. The example simulations show that, especially with step-size adjusting methods, the NRGN method improves the convergence and thus the speed of parallel circuit simulation.