In this paper, the performance analysis of non – preemptive priority M/M/1 queuing model with system breakdown and repair time is examined. We have used the complementary variable method to work out this vector Markov process and investigate the steady state changes that takes place in the equations of the queuing model. The customer length about the two class of customers is also analyzed in this paper based on the system breakdown and repair time. Using little’s formula, the waiting time can also be calculated and the graphical representation is also presented. © 2020, Research Publication. All rights reserved.