The transient electroluminescence of organic light-emitting diodes (OLEDs) with 4,4'-N,N'-dicarbazolylbiphenyl (CBP): fac-tris(2-phenylpyridinate) iridium(III) [Ir(ppy)3] as an emission layer (EML) was investigated. The rise time of these OLEDs was nearly two orders of magnitude longer than the fall time. The highest occupied molecular orbital levels of Ir(ppy)3, lying above that of CBP, act as deep traps for holes, which creates a situation where the hole mobility is much lower than the electron mobility in EML. Semilog plots of the rise time versus voltage applied to OLEDs were almost linear, which could be explained using the dynamic equation of holes and the observed relationship between current and voltage. When the forward bias was applied before the main voltage, the rise time decreased until the bias voltage increased to a certain level. The accumulated charge at the bias onset was consistent with the calculation.