Clathrate hydrates are known to form a thin film along a guest/host boundary. We present here the first report of tetrahydrofuran (THF) clathrate hydrate formation in a THF/water concentration boundary layer. We found that the THF-water system also forms a hydrate film separating the guest/host phases. The lateral growth rate of the film increases as supercooling increases. The thickness of the film at the growth tip decreases as supercooling and the lateral growth rate increase. These tendencies are consistent with reports of experiments for other hydrates and predictions of heat-transfer models. After film formation and slight melting, two types of growth modes are observed, depending on temperature T. At T = 3.0 degrees C, the film slowly thickens. The thickening rate is much lower than the lateral growth rate, as reported for other hydrates. At T <= 2.0 degrees C, however, the growth mode transitions spontaneously from film growth to continuous nucleation, and an agglomerate of small polycrystalline hydrates forms in each phase. Grain boundaries in the film and pore spaces in the agglomerate act as paths for permeation of each liquid. Timing when continuous nucleation starts is dominantly controlled by the time of initiation of liquid permeation through the film. Digital particle image velocimetry analysis of the agglomerate shows that it expands not by growth at the advancing front but rather by continuous nucleation in the interior. Expansion rates of the agglomerate tend to be higher for the cases of multipermeation paths in the film and the thinner film. We suppose that the growth mode transition to continuous nucleation is caused by the memory effect due to slight melting of the hydrate film.