Adding Si3N4 into green emitting Ca3Sc2Si3O12:Ce3+ garnet phosphor generates an additionally red emission band peaking around 610 nm that are assigned to Ce3+ ions having N3− in their local coordination. The excitation spectrum of the red band consists of not only a distinct band at 510 nm of itself but also an intense blue band at 450 nm that belongs to the typical Ce3+ ions with green emission, indicating a notable energy transfer from the green emitting Ce3+ ions to the red ones. The energy transfer significantly enables the achievement of a broad emission spectrum covering a red and green spectral region suitable for generating white light upon a blue light-emitting diode (LED) excitation. The decay patterns of the red and green fluorescence are discussed in relation to the effect of energy transfer. A white LED with high color rendering of 86 and low correlated color temperature of 4700 K is fabricated using the present single garnet phosphor.