The mechanism of diamond growth from an oxy-acetylene flame is discussed using a numerical simulation which includes both gaseous reactions in the low-temperature boundary layer near the substrate and detailed surface reactions on the growing film. It is found from these simulations that the CH3-precursor model is sufficient to explain the growth rate for wide ranges in the substrate temperature T(s) and the gas mixture ratio, and that the fractional density of the surface adsorbing bond (the overall sticking probability) is about 10(-3) at T(s) = 1250 K. It is also shown that the growth rates for other deposition methods are satisfactorily explained by the present model.