Low fuel regression rate is the main drawback of hybrid rocket which should be overcome. One of the improvement techniques to this problem is usage of a solid fuel grain with a complicated geometry port, which has been promoted owing to the recent development of additive manufacturing technologies. In the design of a hybrid rocket fuel grain with a complicated geometry port, the understanding of fuel regression behavior is very important. Numerical investigations of fuel regression behavior requires a capturing method of solid fuel surface, i.e. gas-solid interface. In this study, level set method is employed as such a method and the preliminary numerical tool for capturing a hybrid rocket solid fuel surface is developed. At first, to test the adequacy of the numerical modeling, the simulation results for circular port are compared to the experimental results in open literature. The regression rates and oxidizer to fuel ratios show good agreements between the simulations and the experiments, after passing enough time. However, during the early period of combustion, there are the discrepancies between the simulations and the experiments, owing to transient phenomena. Second, the simulations of complicated geometry ports are demonstrated. In this preliminary step, a star shape is employed as complicated geometry of port. The slot number effect in star port is investigated. The regression rate decreases with increasing the slot number, except for the star port with many slots (8 slots) in the latter half of combustion. The oxidizer to fuel ratio increases with increasing the slot number.