In order to study the influence of the priority queueing policy and different types of input flows on the retrial queueing model indexes in communication networks, this paper constructs a retrial queueing model with non-preemptive priority in which arrival processes of ordinary and priority customers are different arrival rate Markov processes. The main queueing indexes and system steady state condition of the system are derived by the quasi birth-and-death process and matrix analysis. By means of numerical simulation, we found that Markov arrival input flows are more likely to lead to congestion of the system than Poison input flows do, and the priory customer arrival rate is more likely to lead to congestion of the system than the ordinary customers do.