We report on the synthesis of highly fluorescent red-emitting InP quantum dots (QDs) and their application to the fabrication of a high-efficiency QD-light-emitting diode (QLED). The core/shell heterostructure of the QDs is elaborately tailored toward a multishelled structure with a composition-gradient ZnSeS intermediate shell and an outer ZnS shell. Using the resulting InP/ZnSeS/ZnS QDs as an emitting layer, all-solution-processible red InP QLEDs are fabricated with a hybrid multilayered device structure having an organic hole transport layer (HTL) and an inorganic ZnO nanoparticle electron transport layer. Two HTLs of poly(9-vinlycarbazole) or poly[(9,9-dioctylfluorenyl-2,7-diyl)-co-(4,4'-(N-(4-sec-butylphenyl))diphenyl-amine), whose hole mobilities are different by at least three orders of magnitude, are individually applied for QLED fabrication and such HTL-dependent device performances are compared. Our best red device displays exceptional figures of merit such as a maximum luminance of 2849 cd/m2, a current efficiency of 4.2 cd/A, and an external quantum efficiency of 2.5%.