Semantic communication is a promising direction for the future of communication systems. Synonyms act as crucial bridges between semantics and syntax. Inspired by this, this paper introduces a semantic Markov chain model based on state synonymous mapping. This paper demonstrates that the syntactic Markov chain can be transformed into a semantic Markov chain through synonymous mapping. The stationary distribution of the semantic Markov chain can be obtained by partly summing the stationary distribution of the syntactic Markov chain. Similarly, the transition probability of the semantic Markov chain can be obtained by performing a weighted summation of the transition probabilities of the syntactic Markov chain. Additionally, we theoretically proves that the sequence entropy and the entropy rate of the semantic Markov source are no more than those of the syntactic Markov source.