It is highly desirable to red shift the emission of Y3Al5O12:Ce3+ phosphor to obtain a warmer correlated color temperature (CCT) in applications for blue-light pumped white-light emitting diodes (w-LEDs) with high color rendering index (CRI). In this paper, we report the red-shifted emission of Y3MgSiAl3O12:Ce3+ garnet phosphor for w-LEDs through a chemical unit cosubstituting in a solid solution design strategy. The fabrication temperature of the Y3MgSiAl3O12:Ce3+ powder was optimized at 1600 °C, and its structure, photoluminescence property, micromorphology, decay curve, quantum yield, as well as the thermal stability of the samples are investigated in detail. The as-prepared Y3MgSiAl3O12:Ce3+ phosphors display a broad excitation band ranging from 300 to 520 nm (centered at 450 nm) and present an intense Ce3+ 5d–4f emission band in the yellow light region (λem = 564 nm, obviously red-shifted away from Y3Al5O12:Ce3+). This can be explained by the increase of the crystal-field splitting in the Ce3+ 5d levels owing to the chemical unit cosubstitution of Al3+(I) and Al3+(II) ions by Mg2+ and Si4+ ions. The quantum yield of the Y2.92MgSiAl3O12:0.08Ce3+ phosphor is measured as 61.8%. Further investigation on a lamp packaged w-LEDs combining Y2.92MgSiAl3O12:0.08Ce3+ phosphors on a blue InGaN chip shows it to exhibits a lower CCT and higher CRI compared to those of the commercial Y3Al5O12:Ce3+-based devices, indicating their appealing strengths for potential applications in w-LEDs.