Two-dimensional axisymmetric simulations for counterflow nonpremixed methane-air flames were undertaken as an attempt to reproduce the experimentally observed electro-hydrodynamic effect, also known as the ionic wind effect, on flames. Incompressible fluid dynamic solver was implemented with a skeletal chemical kinetic mechanism and transport property evaluations. The simulation successfully reproduced the key characteristics of the flames subjected to DC bias voltages at different intensity and polarity. Most notably, the simulation predicted the flame positions and showed good qualitative agreement with experimental data for the current-voltage curve. The flame response to the electric field with positive and negative polarity exhibited qualitatively different characteristics. In the negative polarity of the configuration considered, a non-monotonic variation of the current with the voltage was observed along with the existence of an unstable regime at an intermediate voltage level. With positive polarity, a typical monotonic current-voltage curve was obtained. This behavior was attributed to the asymmetry in the distribution of the positive and negative ions resulting from ionization processes. The present study demonstrated that the mathematical and computational models for the ion chemistry, transport, and fluid dynamics were able to describe the key processes responsible for the flame-electric field interaction.