Cold thermal energy storage, as a promising way of peak-shifting, can store energy by using cheap electricity during off-peak hours and regenerate electricity during peak times to reduce energy consumption. The most common form of cold storage air conditioning technology is ice on the coil energy storage system. Most of the previous studies so far about ice on coil cold storage system have been done experimentally. Numerical modeling appears as a valuable tool to first better understand the melting process then to improve the thermal performance of such systems by efficient design. Hence, this study aims to simulate the melting process of phase change materials in an internal melt ice-on-coil thermal storage system equipped with a coil tube. A three-dimensional numerical model is developed using ANSYS Fluent 18.2.0 to evaluate the dynamic characteristics of the melting process. The effects of operating parameters such as the inlet temperature and flowrate of the heat transfer fluid are investigated. Also, the effects of the coil geometrical parameters—including coil pitch, diameter, and height—are also considered. Results indicate that conduction is the dominant heat transfer mechanism at the initial stage of the melting process. Increasing either the inlet temperature or the flowrate shortens the melting time. It is also shown that the coil diameter shows the most pronounced effect on the melting rate compared to the other investigated geometrical parameters.