Abstract: By using limit distribution of Markov skeleton processes, the article studies homogeneous denumerable semi-Markov processes and obtains their limit distribution. When the distribution of renewal interval is non-lattice, the result obtained in this paper is consistent with that in ,but the approaches this article used are Markov skeleton processes approaches which differ from .Furthermore, when the distribution of renewal interval is lattice, this paper gives the result, whereas didn't study this case. Finally, this article generalizes the limit distribution of homogeneous denumerable semi-Markov processes, and illustrates the result through one example.