In order to understand the structural and electronic properties of titanium oxide nanoparticles of different sizes, the FIRE algorithm combining the simulated annealing method is employed to find the structures of TinO2n (n=1¡Ð6) nanoparticles with the global minimum potential energy. To deeply understand electronic properties, the relaxation structures of TinO2n (n=1¡Ð6) nanoparticle from previous method will be recalculated by density functional theory (DFT) method. The Fukui function, Frontier Molecular Orbital and density of state of TinO2n (n=1¡Ð6) nanoparticles are discussed for understanding the size effect of TiO2 nanoparticles on chemical reactivity. The adsorption and dissociation energy mechanism of the HN3 molecule and its fragments are also discussed and are compared with the mechanism about HN3 on the anatase surface.