This work presents the results of two-dimensional modeling of the electrode geometry effects on H2/air ignition in a nanosecond plasma discharge. A new multi-scale adaptive reduced chemistry solver for plasma assisted combustion (MARCS-PAC) is applied to simulate the effects of electrode shape, diameter and gap size on ignition enhancement. The results show that a cylindrical electrode produces larger ignition kernel compared with spherical and parabolical electrodes by generating a larger discharge volume with active species and gas heating. There exists a non-monotonic dependence of ignition kernel volume on electrode diameter and gap size. This work provides insights to understand the effects of electrode geometry on the optimization of ignition enhancement in advanced engines.