A cellular automaton (CA) model was developed to describe microstructural evolution of pure substance. A self-consistent interface energy conservation was used to determine the growth velocity of solid-liquid interface instead of the KGT model as is commonly used in previous CA models. The mesh and time dependency of the morphological evolution was also investigated, and the stability of the model was validated. The free dentritic growth of pure succinonitrile in the undercooled melt was simulated by the present model. The results were compared with Glicksman's isothermal dendtitic growth experiment and LMK marginal stability theory. The model reproduced qualitatively most of the dendritic features observed experimentally. The results were in good agreement with theoretical and experimental results.