In order to develop advanced low temperature storage systems based on slurry ice, resistant to recrystallization, Antifreeze Protein (AFP) has been introduced as an effective additive. In this paper, the mechanism of crystal growth when AFPs are adsorbing to the surface of ice has been investigated by Molecular Dynamics simulation. Liquid water molecules were located above the adsorption plane, containing a simplified model of the AFP and the growth potential, corresponding to a supercooling of approximately 40 K was applied. Growth was not easily occurring close to the AFP but at sites where the molecules easily could generate at least two hydrogen bonds to the crystal lattice. This resulted in a curved ice surface, similar to the previously observations using a Scanning Tunneling Microscope.