In order to understand the impacts of dielectric barrier on the discharge characteristics of a nanosecond pulsed surface dielectric barrier discharge (NS-DBD), the effects of dielectric constant and dielectric barrier thickness are numerically investigated by using a three-equation drift–diffusion model with a 4-species 4-reaction air chemistry. When the dielectric constant increases, while the dielectric barrier thickness is fixed, the streamer propagation speed (V), the maximum streamer length (L), the discharge energy (QD_ei), and the gas heating (QGH) of a pulse increase, but the plasma sheath thickness (h), the fast gas heating efficiency η, and the charge densities on the wall surface decrease. When the dielectric barrier thickness increases, while the dielectric constant is fixed, V, L, QD_ei, and QGH of a pulse decrease, but h, η, and the charge densities on the wall surface increase. It can be concluded that the increase of the dielectric constant or the decrease of the dielectric barrier thickness results in the increase of the capacitance of the dielectric barrier, which enhances the discharge intensity. Increasing the dielectric constant and thinning the dielectric barrier layer improve the performance of the NS-DBD actuators.