An observation of gas hydrate growth process outside of a horizontal heat transfer tube in the reaction system of 0.2% SDS water solution and HCFC141b is carried out in a transparent apparatus of gas hydrate indirect-contact heat transfer mode reactor. The morphology of gas hydrate growth process is described according to the recorded photos and temperatures. It is found that the gas hydrate grows mainly in the liquid HCFC141b phase, which is different from the growth morphology of icearound the heat transfer tube. In the light of the mechanism analysis using the theory of surface free energy, the cause lies in that the water solution can permeate spontaneously into the liquid HCFC141b phase along the surface of heat transfer tube under the effect of surface tension, so it is reasonable that the gas hydrate growth process can be improved if vertical metal fins are added to the heat exchanger in the indirect-contact heat transfer model of gas hydrate cool storage vessel.