Abstract: In this paper, a class of continuous time Markov chain model for recombinant cell chemostat culture is investigated. Firstly, applying the cumulant generating function, the moment equations which the digital features satisfy are obtained. Then the moment closure equations are derived by the moment closure techniques based on the lognormal approximation, and the corresponding It$\hat{\rm o}$ stochastic differential equations are given according to the Euler-Maruyama method. To illustrate the rationality of the moment closure, the numerical simulation is given to compare the deterministic model with the stochastic model and moment closure equations，and to analyze trends of the recombinant cell. The result shows that the behaviour of random work is consistent with the corresponding deterministic model.

Key words: continuous time Markov chain, cumulant generating function, lognormal, moment closure, It$\hat{\rm o}$ stochastic differential equations