A physically based mathematical model for the charge transport in field-effect transistors and lighting-emitting diodes based on disordered organic semiconductors has been presented. It is developed basing on the Gaussian disorder model and extends the pioneering work of Pasveer et al. [Phys. Rev. Lett. 94, 206601 (2005)] to higher carrier densities and large electric field. The experimental current voltage characteristics in devices based on semiconducting polymers are excellently reproduced with this model. Furthermore, we calculate and analyze some electrical properties for the relevant polymers in detail using this model.