The paper analyzes the M/M/1/N single working vacation queueing system with setup time and server breakdowns. In this system, the server works at a lower service rate instead of stoping working completely during the vacation period. It is assumed that the server is subject to breakdown. The server stops services for customers and is repaired immediately when a breakdown occurs. Both the breakdown time and the repair time for the server follow exponential distributions, and they have different values in the working vacation period and regular busy period respectively. Meanwhile, the setup time from shut down period to regular busy period follows exponential distribution too. We establish the finite quasi birth and death(QBD) process of the system. Matrix-geometric approach is utilized to develop the interdependent rate matrix of the QBD, which helps to get the steady state probability vector. The fundamental matrix and covariance matrix of the system are obtained through the infinitesimal generator of the finite QBD and the steady state probability vector. With the fundamental matrix and covariance matrix, the steady state performances of the system, such as the output variance, availability, throughput, the queue length and fault frequency of the system, are obtained. Numerical analysis shows the effectiveness and feasibility of the proposed approach. Meanwhile, sensitivity analysis studies the influence of the parameters on the performances of the system, which provides a good theoretical basis for the practical application of the proposed model.