Non-equilibrium plasma has promising applications in combustion enhancement. In this study, 1D simulations are conducted for the forced ignition process using non-equilibrium plasma generated by repetitively pulsed nanosecond discharge (NSD). The ignition kernel is induced by a discharge area with NSD and it develops and propagates in a static stoichiometric hydrogen/air mixture. The objective is to assess how the characteristics of NSD affect the ignition delay time and ignition kernel development during the forced ignition process. Similar to the homogeneous ignition considered in part I, the forced ignition process is found to be strongly affected by the pulse number, discharge frequency, discharge radius, total input energy, and input energy per pulse of NSD. For a fixed input energy per pulse, the ignition delay time decreases and the propagation speed of the initial ignition kernel increases with the pulse number, discharge frequency and discharge radius. However, for a fixed total input energy, the ignition delay time increases and the propagation speed of the initial ignition kernel decreases with the pulse number. Furthermore, it is found that the promotion of ignition kernel development and propagation in the forced ignition by NSD are mainly due to the kinetic effect rather than the thermal effect.