With reference [4] relating to the queuing model of M/M/1 in a random environment, this paper poses and deals with the queuing Model of M/M^Y/1 in a random environment. ln statistical equilibrium, the author obtains the equilibrium distribution of queue length and that of waiting queue length, the average of queue length and that of waiting queue length as well as the equilibrium distribution of waiting time and that of staying time, the average of waiting time and that of staying time.