Abstract: The authors constructed the almost periodic point dense system based on minimal mapping，studied  the relation between the almost periodic point dense system and Li-Yorke chaos by using topological transitivity and density,and  proved the topological ergodicity of the almost periodic points dense system under certain conditions.The study established the relation between the almost periodic point dense system and topological ergodicity，and had some enlightenments on the further studying of the characteristics of the measure centre of the almost periodic points dense system.

Key words: almost periodic points, transitive, topological ergodicity