Abstract: Arriving customers who find the server busy join the infinite priority queue with probability q and join the infinite retrial group (orbit) with complementary probability p in accordance with an FCFS discipline. The necessary and sufficient condition for the stability of the system is obtained, assuming that only the customer at the head of the orbit is allowed to retry for service and considering the factor of server breakdowns. The steady-state distributions of the numbers of customers in the priority queue, the orbit, and the system are obtained, along with average waiting times with the method of VMP. The main reliability indices of server, the probability that the server is idle, the service and the repair are also derived.