This　paper　focuses　on　a　differential　equation　logistic　model　simulating　tumor　growth.　We　design　a　kind　of　tumor　dynamic　growth　model　with　one-dimensional　cellular　automata.　A　discrete　logistic　model　is　developed　from　the　continuous　logistic　model.　Based　on　others＇　work,　we　design　discrete　mathematical　growth　dynamic　model　with　cellular　automaton.　In　terms　of　discrete　model,　we　design　stochastic　evolving　rules　of　cellular　automaton.　And　this　paper　simulates　the　tumor　growth　dynamic　model　with　cellular　automata.　The　theoretic　analysis　and　results　of　cellular　automaton　model　are　in　agreement　with　data　from　the　ideal　differential　equation　logistic　growth　of　cancer.