Recently, the Cox-Ingersoll-Ross (CIR) model with Markov switching has been discussed extensively. However, the covariance function and the kth moment for this model are still open. In this paper, we consider some characterizations for the CIR model with Markov switching. First, the conditional moment generating functions for CIR model with Markov switching are given. Then, explicit expressions for the covariance function and moments of the CIR model with Markov switching are obtained. Finally, several examples have been presented to illustrate our results.