This　paper　focuses　on　simulating　tumor　growth　with　cellular　automaton(CA),　in　which　a　one-dimensional　CA　is　designed　based　on　the　logistic　model.　First,　a　discrete　logistic　model　is　derived　from　the　continuous　logistic　model　and　implemented　with　the　one-dimensional　CA.　And　then,　the　random　evolution　rules　of　CA　are　derived　according　to　the　discrete　model.　Finally,　a　CA　model　is　applied　to　simulate　tumor　growth.　Theoretic　analysis　and　experimental　results　of　the　one-dimensional　CA　are　in　good　agreement　with　the　data　from　the　ideal　logistic　growth　of　cancer.