In this paper we present a new algorithm, based on Kirchhoff's Current Law (KCL) verification, for assessing convergence in circuit-level simulation and its implementation in the NGSPICE open source circuit simulator. We start from the analysis of false convergence problems appeared in the analysis of test circuits that we found to be related to the convergence checks that NGSPICE simulator inherits from SPICE3F5. These checks are inaccurate in some cases, so we propose to replace them with a new, efficient, algorithm based on KCL verification. The methodology to verify KCL of the circuit is detailed in this paper, along with the extraction flow, required to compute every KCL contribution. We finally present a case study of a circuit showing non converging solution, while the same circuit can be solved using the proposed algorithm. © 2014 IEEE.