In this work, the anataze phase of TiO<sub>2</sub> nanoparticles was prepared by sol gel method. We changed time and temperature of calcinations to change size and property of nanoparticles. The Transmission Electron Microscopy and Scanning Electron Microscopy were used for characterization of the TiO<sub>2</sub> nanoparticles. The nanoparticle size was increased with time and temperature. We found that the average size of samples was changed from 30 to 46 nm with changing temperature from 450℃ to 650℃ and at fixed temperature (450℃) with changing of calcination times from 1 to 3 hours, the size was changed from 30 to 58 nm. For study the dynamic of nanoparticles, the TiO<sub>2</sub> nanoparticles were added to water with 2.4 weights present of particles to the water. The different size of TiO<sub>2</sub> nanoparticles was studied with photon correlation spectroscopy. The relaxation time was increased with increasing of nanoparticle size and so diffusion coefficient was decreased