Based on the physical processes of solute diffusion and interfacial energy, a model of describing crystal growth was developed with the improvement of algorithm of solute redistribution and the improved discretization scheme of partial derivative of liquid concentration at the interface, including the effects of constitutional undercooling, curvature undercooling, anisotropy of interfacial energy and perturbation on the interface. By using this model, cellular automata method was adopted to simulate morphology evolution of the three typical interface including planar, cellular and dendritic in aluminum alloy directional solidification. By comparing the simulation parameters and results in this model with in the classical solidification theory, it was discovered that the planar interface was formed when the G/V value was slightly smaller than the critical value given by constitutional undercooling criterion. The variation relationship of the average primary dendrite spacing with the temperature gradient and the drawing velocity were studied and matched well with the theoretical results.