This study investigates the effects of voltage rise rates from 0.1 kV ns(-1) to 100 kV ns(-1) on streamer discharge in air at atmospheric pressure using numerical simulation. The curvature of the needle electrode is also used as an input parameter to change the streamer inception voltage and the average voltage, V (ave), during streamer propagation. The results show that the streamer propagation velocity, v (pri), the electric field strength at the streamer head, E (h), the diameter of the streamer channel, and the O radical production characteristics during the primary streamer propagation are dependent on V (ave). v (pri) and E (h) exhibit different effects on V (ave)/d, where d is the gap distance of the electrode, which indicates that the streamer remains in the transient state from the filament-type discharge to the diffuse-type discharge. The comparison between the simulation and experimental results shows that the simulated v (pri) characteristics are in good agreement with the experimental results, regardless of the voltage waveform and electrode configuration, which indicates that V (ave)/d has a strong correlation with the primary streamer characteristics.