To model the carrier transport in organic light-emitting diodes (OLEDs) with random dopant effects in the emitting layer, two-dimensional simulation was used. By including the Gaussian shape density of states and field-dependent mobility in the Poisson and drift-diffusion solver, the carrier transport, trapping in the dopant state, and radiative recombination were accurately modeled. To examine the model, the current-voltage characteristics of organic light-emitting devices were compared. The host material in the emitting layer was 2,2-bis(1-phenyl-1H-benzo[d]imidazol-2-yl)biphenyl (BImBP), which was doped with bis[2-(4,6-difluorophenyl)pyridinato-C2,N](picolinato)iridium(III) (FIrpic) at various concentrations. By including the random doping model, the trend of mobility was altered and the radiative efficiency fitted experimental values well.