By integrating cellular automaton (CA) theory into topology optimization of continuum, the local rule is defined for sensitivity analysis and updating of the design variable, according to the analysis of the structural mechanical response. Topology optimization design of loaded structure is conducted using minimal compliance as the optimization objective. The optimal distribution of material in the design domain is finally obtained. Comparing to other algorithms, the local rule has proved to be computationally efficient to solve structural topology optimization problems. The resulting optimal structures are free of numerical instabilities such as the checkerboard patterns and mesh dependency.