Abstract: Based on the study of logistic model simulating tumor growth, a kind of tumor dynamic growth model is designed. From the continuous logistic model its discrete differential form is derived, and from the predecessors' work a discrete dynamic computer growth model with cellular automata and the stochastic evolving rules of artificial cellular automata are designed. Through the numeric emulation experiment of tumor growth model with one dimension artificial cellular automata, it is known that the theoretic analysis and experiment results are in agreement with data from the logistic growth of cancer.