Broadband dielectric spectroscopy measurements were performed on partially crystallized gelatin-water mixtures with gelatin concentrations of 1-5 wt % for temperatures between 123 and 298 K to study the dynamics of ice. These systems contain only hexagonal ice. Nevertheless, four dielectric relaxation processes of ice were observed. At temperatures below the crystallization temperature, a loss peak was observed, and it separated into four loss peaks at around 225 K. Using the temperature and concentration dependencies of these relaxation processes, we confirmed that these four processes originated from ice. For the relaxation time of ice, τice, the deviation of the temperature dependence of τice from the Arrhenius type is larger for the relaxation process at the higher-frequency side. For the temperature dependence of τice for the dominant process, three temperature ranges with different activation energies, Ea, were investigated. The intermediate-temperature range of τice with the smallest Ea decreased as the gelatin concentration increased; therefore, τice of the dominant process changed from the relaxation process with the smaller τice to that with the larger τice as the gelatin concentration increased. In addition, the relaxation process of ice with larger τice values was found to have larger values of Ea. These results suggest that a higher gel network density affects the temperature dependence of τice.