Abstract: To study the M/M/N repairable queue system with one repairman and nonpreemptive priority,in which the rates of server breakdown are different between busy time and idle time,the differential equations of this system are obtained by receiving the state transition diagram.By using the QBD(quasi birth and death process) method,the steady-state condition is got,and then the steady-state balanced equations are obtained.By analysing,the thinking of solving the key steady probability is got.Because of the complexity of calculating the steady probability by handwork when N≥2,the steady probability,can be obtained by using Mathematica software,and a numberical example is given.On the basis of deriving the steady probability,two indices,the steady state distribution of the number of effective servers and the moment generating function of the steady state queue length,are also given.