We report on the enhancement of the electrical photoresponse in a hybrid structure composed of multi-layer graphene flakes covered by a layer of CdSe/ZnS quantum dots (QDs) and placed between metal electrodes. The rate of the photoexcitation energy transfer from QDs to graphene, (0.5-2) x 10(9) s(-1) which controls the photoelectrical response of the structure, was found from the analysis of photoluminescence intensities and decay times for QDs in solution, on a bare glass substrate and on the surface of multilayer graphene, and in the presence of ammonia vapors. (C) 2015 AIP Publishing LLC.11810 Ministry of Education and Science of the Russian Federation [14.B25.31.0002, 3.109.2014/K]