Some biological substances control the nucleation and growth of inorganic crystals. Antifreeze proteins, which prohibit ice crystal growth in living organisms, promise are also important as biological antifreezes for medical applications and in the frozen food industries. In this work, we investigated the crystallization of ice in the presence of a new cryoprotector, carboxylated epsilon-poly-L-lysine (COOH-PLL). In order to reveal the characteristics and the mechanism of its antifreeze effect, free-growth experiments of ice crystals were carried out in solutions with various COOH-PLL concentrations and degrees of supercooling, and the depression of the freezing point and growth rates of the tips of ice dendrites were obtained using optical microscopy. Hysteresis of growth rates and depression of the freezing point was revealed in the presence of COOH-PLL. The growth-inhibition effect of COOH-PLL molecules could be explained on the basis of the Gibbs-Thomson law and the use of Langmuir's adsorption isotherm. Theoretical kinetic curves for hysteresis calculated on the basis of Punin-Artamonova's model were in good agreement with experimental data. We conclude that adsorption of large biological molecules in the case of ice crystallization has a non-steady-state character and occurs more slowly than the process of embedding of crystal growth units.