We present the first model ever, that describes explicitly ice crystal growth in a sugar solution during freezing. This 2-D model uses the phase field method, supplemented with realistic, and predictive theories on the thermodynamics and (diffusion) kinetics of this food system. We have to make use of a novel type of phase field to obtain realistic, micron-sized ice crystals, and exclusion of sugar from the crystalline phase. Via simulation of a single ice crystal, we identify important time scales governing the growth. These times scales are also important for the coarsening of the ice morphology in freezing systems with multiple ice crystals. These simulations show that the average ice crystal size is governed by the freezing rate via a power law, similar to an empirical relation from literatures, which is deduced from experiment. The presented model is viewed as a good basis for even more realistic simulations of crystal growth in food. (C) 2015 Elsevier Ltd. All rights reserved.