The unit hydrograph (UH) is a hydrological tool that represents the unit response of a watershed to a unit input of rainfall. UH models based on lumped reservoir and channel conceptual cascade assume that rainfall is evenly distributed, thus limiting the use of UHs to relatively small watersheds of less than around 500 km2 in area. In this paper, a new hydrograph prediction method, named the generalized concentration curve (GCC), was derived that can be applied to large heterogeneous watersheds. The GCC method divides the watershed into subareas by isochrones. In each subarea, an independent linear reservoir-channel cascade model that considers both attenuation and translation is established. Comparative application of the GCC and the traditional Nash instantaneous unit hydrograph to 18 storm events from three medium-sized watersheds (727, 1,800 and 5,253 km2 in area) revealed superior performance of the GCC, with the average Nash–Sutcliffe efficiency coefficient higher by 7.66%, and the average peak discharge error lower by 4.14%. This study advances the theory of UH and expands the scope of application of UH to larger watersheds.