The heat transfer enhancement of a latent heat thermal energy storage system with bundled tube structures using air as the heat transfer fluid (HTF) is investigated numerically. Transient simulations of the charging processes are performed based on a two-dimensional numerical model, and the melting processes of the storage units with staggered tube bundle structure and parallel tube bundle structure are compared with that of flat plate structure. The effects of the air mass flow rate and the internal fin arrangement in the staggered tube bundle storage unit are also investigated. The results show that the heat charging rate of the latent heat storage using air as the HTF can be enhanced by increasing the heat transfer surface, the degree of air turbulence and the gas flow rate; and the storage unit with staggered tube bundle structure is a good choice for its larger heat transfer surface and higher degree of air turbulence. It is also found that the internal fin arrangement has some influences on the PCM melting process, and adding internal outside-in fins that are connected to the tube inner wall can effectively enhance the PCM melting.