Abstract: A spherical shape is normally assumed for ice particles in most cloud models. However, the shapes of ice crystals in the real atmosphere are much more complicated. Ice crystal habits will change with the variation in ambient temperature and water vapor saturation. Such habits have been proven as critical parameters impacting cloud simulations. In this study, based on the theoretical model of the deposition growth of an ice crystal, we firstly simulated the growth of a single ice crystal by water vapor deposition under temperatures from -1℃ to -30℃. The model can capture the evolution of axis length (a for prism face;c for basal face), mass and aspect ratio in comparison with the data from wind tunnel observations. We further simulated the water vapor deposition growth of non-spherical ice crystals with the twodimensional positive definite advection transport algorithm (MPDATA). Furthermore, in order to test the feasibility of applying such a treatment into the Eulerian dynamical framework, the mass growth of ice crystals under different bin resolutions for the aspect ratio was simulated. The results showed that the model using the MPDATA method can capture the evolution of ice crystals for both their mass and their aspect ratio. Even though some Lagrangian models with bin microphysics involve microphysical processes for non-spherical ice crystals, their schemes with the hybrid Lagrangian-Eulerian advection transport method cannot be applied into cloud models under the Eulerian dynamical framework, which can simulate more complicated microphysical processes and dynamical processes involved in ice particles.