We have investigated the following surface reactions theoretically, in order to elucidate the mechanism of the initial step of TiN chemical vapor deposition (CVD) on amorphous SiO2 surfaces using TiCl4 and NH3 as material gases: (i) adsorption of TiCl4 and NH3 onto the SiO2 surface; (ii) surface reactions of the Langmuir-Hinshelwood mechanism and the Eley-Rideal mechanism between the adsorbates produced by TiCl4 and NH3; and (iii) reactions of TiCl4 and NH3 with surface OH groups of SiO2. The energetics of these surface reactions were calculated by using the BLYP density functional theory (DFT) with cluster models of amorphous SiO2 surfaces.