We have studied silica single and double chain based on two-membered ring and nanotubes based on three-membered ring using the density-functional theory at 6-31G(d) level. The average binding energy, electronic structure and vibration frequency were calculated. Our calculations show that the average binding energy and energy gap monotonically change with increasing SiO2 units. Infrared spectrum indicated that the frequency and intensity of radial and tangential vibration shift obviously. Radial vibration frequency shifts to high frequency while tangential vibration frequency shifts to low frequency showing the existence of quantum size effect and anisotropic property of vibration in SiO2 nanomaterial.