In the present study, monodispersed CeO2 nanoparticles (NPs) of size 8.5 ± 1.0, 11.4 ± 1.0 and 15.4 ± 1.0 nm were synthesized using the sol-gel method. Size-dependent structural, optical and magnetic properties of as-prepared samples were investigated by X-ray diffraction (XRD), field emission scanning electron microscope (FE-SEM), high resolution transmission electron microscopy (HR-TEM), ultra-violet visible (UV-VIS) spectroscopy, Raman spectroscopy and vibrating sample magnetometer (VSM) measurements. The value of optical band gap is calculated for each particle size. The decrease in the value of optical band gap with increase of particle size may be attributed to the quantum confinement, which causes to produce localized states created by the oxygen vacancies due to the conversion of Ce4+ into Ce3+ at higher calcination temperature. The Raman spectra showed a peak at ∼461 cm-1 for the particle size 8.5 nm, which is attributed to the 1LO phonon mode. The shift in the Raman peak could be due to lattice strain developed due to variation in particle size. Weak ferromagnetism at room temperature is observed for each particle size. The values of saturation magnetization (Ms), coercivity (Hc) and retentivity (Mr) are increased with increase of particle size. The increase of Ms and Mr for larger particle size may be explained by increase of density of oxygen vacancies at higher calcination temperature. The latter causes high concentrations of Ce3+ ions activate more coupling between the individual magnetic moments of the Ce ions, leading to an increase of Ms value with the particle size. Moreover, the oxygen vacancies may also produce magnetic moment by polarizing spins of f electrons of cerium (Ce) ions located around oxygen vacancies, which causes ferromagnetism in pure CeO2 samples.