The thermal expansion is one of the fundamental physical properties of the materials that reflects the anharmonicity of the interatomic potential. The description and understanding of thermal expansion are important in the applications of the materials. From the fundamental science point of view, the thermal expansion in glassy materials is also related directly to the relaxation behavior, a topic of current interest in condensed matter physics. However, the estimation of the thermal expansion coefficient of the materials having complex structures is not easy. In the present study, motivated by a previous work on Lindeman’s like rule between the thermal expansion coefficient and the glass transition temperature, we developed a model for the thermal expansion coefficient of metallic glasses by using a parametrized form of the interatomic potential and the Debye model for the distribution of atomic oscillations. The obtained analytical expression enables us to estimate the temperature dependence of the thermal expansion coefficient just from the glass transition temperature. However, the analysis based on the model indicates that the temperature dependence is weak compared to the experimental data. This observation suggests that we must go beyond the Debye model to treat the thermal expansion of glassy materials.