Researches a sort of random time-change for a Markov chain, which is different from random time-change of ordinary Markov process theory. It is realized by additive functional of the Markov process. The process which will be random time-substituted is a time-discrete, countable state space and time-homogeneous Markov chain, and the process which will be used to substitute is a time-continuous, non-decreasing and space-homogeneous Markov chain with the state-space constituting of non-negative integers, X and are mutually independent. It is proved that the random time-changed process , is a Markov chain, whose transition probabilities are calculated. If is time-homogeneous, then Y is also time-homogeneous.