An atomically thin MoS2 field-effect transistor (FET) is expected as an ultrathin photosensor with high sensitivity. However, a persistent photoconductivity phenomenon prevents high-speed photoresponse. Here, we investigate the photoresponse of a MoS2 FET with a thin Al2O3 buffer layer on a SiO2 gate insulator. The application of a 2-nm-thick Al2O3 buffer layer greatly improves not only the steady state properties but also the response speed from 1700 to 0.2 s. These experimental results are well explained by the random localized potential fluctuation model combined with the model based on the recombination of the bounded electrons around the trapped hole.