Modeling of hydrate growth at the interface between gas and aqueous phases is critical for evaluating the growth rate of hydrate film and initial thickness in the oil and natural gas industries. However, most existing heat transfer models in presumption and hypothesis possess logical or physical deficiencies, which may lead to wide deviations when predicting results. In this work, a new model of hydrate film lateral growth along a planar gas liquid boundary is developed, which considers natural convection heat transfer. This model not only correlates subcooling, which is generally regarded as the main controlling factor in the process of hydrate growth, but also describes a quantitative relation with experimental temperature that has never been embodied in previous models. In combination with the experimental data in this paper and the previous literature, a comparison of the simulation between the proposed model and typical heat transfer models is provided. The simulated results show that this model agrees well with the measured data for both the bubble surface and planar gas liquid interface. Furthermore, estimations of methane hydrate film thickness at a subcooling range of 0.3-3 K are performed using the new model and analyzed in contrast with data available in the literature. This work simultaneously yields a subtle observation and investigation into hydrate film propagation at the diverse position of gas liquid interface and provides new insights into qualitatively characterizing heat transfer efficiency of hydrate film frontier by introducing a dimensionless number beta.