We have carry out numerical simulation of the electric-optical characteristics of organic light emitting diodes with gradient-doped emitting layer which were reported to be effective in improving luminous efficiency and lifetime. In this paper, the basic structure is comprised of ITO/NPB/$Alq_3$:C545T[%]/$Alq_3$/LiF/Al, six devices by separating the emitting layer of $Alq_3$:C545T[%] were studied. As the result, the uniformly-doped devices exhibited superior luminous efficiency-current density characteristics over conventional undoped device. In the case of gradient-doped devices, electric-optical characteristics were improved similar to uniformed-doped devices, unusually the distribution of traped-charge density in the OLED devices was shown as the staircase.