Abstract: In this paper, a repairable system with a repairman who has multiple jobs was studied. If the system fails and the repairman is working, it will wait for repairing until the repairman is available. When the repairman is available, the system has priority. After repairing, the system is not "as good as new". Under these assumptions, using the supplementary variable method and the geometric process, some important indexes were derived, such as the system reliability, availability, rate of occurrence of failures, etc. Finally, a numerical example was given to illustrate our results.