A series of experiments were carried out to measure, with the aid of direct observations through a high-resolution optical microscope, the local thickness of a ring-shaped hydrate film formed over the surface of each discoid drop of HCFC-141b (CH3CCl2F) held stationary in a narrow liquid-water channel confined by two transparent, parallel plates, while the experimental system was controlled at a temperature below the hydrate/liquid-water/liquid-HCFC-141b equilibrium temperature, T-tri, at atmospheric pressure. It was revealed that the thickness may be significantly different from place to place over the same hydrate film and that the thickness at each location decreases with an increase in the water flow rate and with a temperature rise. To clarify the dependency of the local film thickness thus measured on the convective mass transfer of the hydrate-guest substance from the film surface to the water flow, we performed numerical simulations of the convective mass transfer and also chromatographic measurements of the solubility of HCFC-141b in liquid water so that we could predict the local mass transfer coefficient and the mass flux of the hydrate guest, HCFC-141b, at any location along the hydrate-film/liquid-water interface. Plotting the film-thickness data obtained at each temperature level against relevant predictions of the mass transfer coefficient or the mass flux, we found the film thickness to be nearly inversely proportional to the mass transfer coefficient or the mass flux. This finding supports the idea that the film thickness is determined by the balance between the rate of hydrate-crystal dissociation induced by the aforementioned convective mass transfer and the rate of hydrate-crystal formation depending on the liquid-water permeation into the hydrate film.