Synthesis of pure Hafnium Oxide (HfO₂), and HfO₂ doped with Gadolinium (1, 3, 5 and 7 mol%) nanoparticles (NPs) had been carried out by Precipitation and co-precipitation method using the precursor solution of Hafnium (IV) chloride (HfCl₄) and Gadolinium(III) chloride hexahydrate (GdCl₃·6H₂O) with Sodium hydroxide (NaOH) which was dissolved in deionized water. The synthesized compound was characterized and analyzed by X-ray diffraction (XRD), Field emission scanning electron microscopy (FESEM), Energy dispersive X-ray analysis (EDX), UV-visible spectrophotometer, Photoluminescence (PL), Fourier Transform infrared spectroscopy (FTIR) and Raman spectroscopy. The result from X-ray diffraction showed that the Gd3+ concentration for 7 mol% had attended directly crystalline phase of Cubic HfO₂ structure. Morphology and element analysis of the samples were analyzed using FESEM and EDX, which indicated cluster formation, fluffy and voids with highly agglomerated particles and EDX exhibited no extra peaks with other than constituent elements present in extrinsic HfO₂. From UV Spectra it was observed that the optical band gap of both Intrinsic and extrinsic of HfO2 NPs were found to be 5.74 eV, 3.62 eV, 3.69 eV, 3.78 eV and 4.19 eV. The Photoluminescence Spectra showed the 313 nm emission line which might be due to 6P7/2→8S7/2 transition and the Raman Spectra clearly represented the monoclinic structure by showing the presence of Ag and Bg Modes and cubic structure because of the presence of F2g mode.