A physical-mathematical model of dependence of internal quantum efficiency on current for LED structures with quantum wells has been developed. The volt-ampere characteristic is modelled with the involvement of Shockley, Noyce, Sah recombination theory, supplemented by the quantum wells distribution function. In order to obtain dependence of internal quantum efficiency of LEDs on current, model of rate of ABC recombination in quantum wells is used. The developed model was tested with variations of quantum wells parameters and external impact conditions.