$Ce^{3+}$-doped yttrium aluminum gallium garnet (YAGG:$Ce^{3+}$), which is a green-emitting phosphor, was synthesized by solid state reaction using ${alpha}$-phase or ${gamma}$-phase of nano-sized $Al_2O_3$ as the Al source. The processing conditions and the chemical composition of phosphor for the maximum emission intensity were optimized on the basis of emission intensity under vacuum UV excitation. The optimum heating temperature for phosphor preparation was $1550^{circ}C$. Photoluminescence properties of the synthesized phosphor were investigated in detail. From the excitation and emission spectra, it was confirmed that the YAGG:$Ce^{3+}$ phosphors effectively absorb the vacuum UV of 120-200 nm and emit green light positioned around 530 nm. The crystalline phase of the alumina nanoparticles affected the particle size and the luminescence property of the synthesized phosphors. Nano-sized ${gamma}-Al_2O_3$ was more effective for the achievement of higher emission intensity than was nano-sized ${alpha}-Al_2O_3$. This discrepancy is considered to be because the diffusion of $Al^{3+}$ into $Y_2O_3$ lattice is dependent on the crystalline phase of $Al_2O_3$, which affects the phase transformation of YAGG:$Ce^{3+}$ phosphors. The optimum chemical composition, having the maximum emission intensity, was $(Y_{2.98}Ce_{0.02})(Al_{2.8}Ga_{1.8})O_{11.4}$ prepared with ${gamma}-Al_2O_3$. On the other hand, the decay time of the YAGG:$Ce^{3+}$ phosphors, irrespective of the crystalline phase of the nano-sized alumina source, was below 1 ms due to the allowed $5d{ ightarrow}4f$ transition of the $Ce^{3+}$ activator.