YAG:$Ce^{3+}$ phosphor powders were synthesized using $Al(OH)_3$ seeds by means of a PVA-polymer-solution route. Various types of PVA with different molecular weights (different polymerization) were used. All dried precursor gels were calcined at $500^{circ}C$ and then heated at $1500^{circ}C$ in a mix of nitrogen and hydrogen gases. The final powders were characterized via XRD, SEM, PSA, PL, and PKG analyses. The phosphor properties and morphologies of the synthesized powders were dependent on the PVA type. As the molecular weight of the PVA was increased, the particle size gradually decreased with agglomeration, and the luminous intensity of the phosphor increased. However, the phosphor powder prepared from the PVA exhibiting very high molecular weight, showed a 531 nm (blue) shift from the 541 nm (yellow) wavelength of the YAG:$Ce^{3+}$ phosphor. Finally, the synthesized YAG:$Ce^{3+}$ phosphor powder prepared from the PVA with 89,000 - 98,000 molecular weight showed phosphor properties similar to those of a commercial phosphor powder, but without a post-treatment process.