In this paper, we study the effect of red LED illumination on the positive magnetoresistance of a high-mobility two-dimensional electron gas in a selectively doped GaAs/AlAs heterostructure at a temperature T = 4.2 K in magnetic  fields B < 1 T. We observe a significant increase in the positive magnetoresistance as a result of illumination. It is shown that illumination-induced increase in the positive magnetoresistance in the two-dimensional electron system  under study is due to an increase in the quantum lifetime.