The optical properties of dielectric homogeneous nonmagnetic vanadium dioxide (VO2) nanospheres are studied theoretically for a 20 nm diameter in air (n = 1) and for different diameters between 20 and 240 nm in water (n = 1.33). The absorption, scattering and extinction efficiencies are calculated for VO2 nanospheres by using the Metallic Nanoparticle Boundary Element Method (MNPBEM) toolbox. It is calculated the extinction efficiency of a 20 nm diameter VO2 nanosphere in the air for metallic phase. The Localized Surface Plasmon Resonance (LSPR) which looks like in noble metals as predicted is found in the NIR region. The shape and position of a 20 nm diameter VO2 nanosphere's LSPR is discussed in a qualitative manner. The absorption, scattering and extinction efficiencies of the VO2 nanosphere with varying diameters are investigated systemically in water for the metallic phase. The relative contributions of the absorption and scattering efficiencies in the metallic state are discussed to the extinction efficiencies. The results indicated that absorption is the dominant process in the wavelength range of 300-2400 nm. In addition to the LSPR, a Mie Resonance peak was found in the visible region for VO2 nanospheres with diameters bigger than 100 nm. The infrared switching properties of the VO2 nanospheres are investigated by calculated extinction efficiencies with various diameters in water for the metallic and insulating phases. The smart window parameters such as luminous transmittance and solar modulation are discussed in terms of extinction efficiencies of metallic and insulating phases which can be a guide to find the optimum diameter of VO2 nanosphere in application. The LSPR intensity is investigated with varying diameters of the nanospheres at the wavelength at which the LSPR is seen. It is found that the LSPR intensity is almost constant up to 60 nm diameter and decreases rapidly in between 60 and 240 nm diameter of VO2 nanospheres. The size dependency of the LSPR peak of the VO2 nanospheres is also investigated systematically. There is a red-shift from 1096 to 1324 nm in the LSPR peak values and broadening from 760 to 900 nm in the LSPR's FWHM that shows also broadening in LSPR bandwidth while increasing the diameter of VO2 nanosphere from 20 to 240 nm. It is found that the LSPR's peak position changes exponentially with the diameter and FWHM changes almost linearly for the diameter values studied.