Initial growth processes of hydrogenated amorphous silicon (a-Si:H) on a glass surface have been studied by an ab-initio molecular-orbital method on the reactions between surface model compounds and gas phase species. The process defined here as the initial process is the reaction to bind SiH3, the main precursor to a-Si:H, to a functional group in the surface model compounds (3)(HO)Si-O-R where R represents H, Si(OH)(3), B(OH)(2), B(OH)(3)(-), SiH3 and Si(OH)(3)OSiH3. Negative enthalpy (Delta H) and Gibbs' free energy (Delta G) changes at standard state (298.15 K, 1 atm) were obtained by the calculation for the hydrogen substitution in = Si-OH or =B-OH with SiH3 to form = Si-O-SiH3 or = B-O-SiH3, respectively. This spontaneous first step can be followed by the two step propagation reaction which is also energetically favorable, to form an Si-Si bond: -O-SiH3 + H --> -O-SiH2 + H2 up arrow -O-SiH2 + SiH3 --> -O-SiH2-SiH3 Due to the presence of OH bonds in high density on the whole area of glass surface, these initiation and propagation should occur everywhere to deposit a-Si:H homogeneously on a glass substrate. Thus, the calculation is consistent with the surface morphology observed by AFM.