ATM switch handles the traffic for a wide range of appliations with different QOS(Quality-of-Service) requirements. In ATM switch, the priority control mechanism is needed to improve effectively the required QOS requirements. In this paper, we propose a priority control mechanism using the cell transfer ratio type and discard threshold in order to archive the cell loss probability requirement and the delay requirement of each service class. The service classes of our concern are the service class with high time priority(class 1) and the service class with high loss priority control mechanism, cells for two kind of service classes are stored and processed within one buffer. In case cells are stored in the buffer, cells for class 2 are allocated in the stored and processed within one buffer. In case cells are stored in the buffer, cells for class 2 are allocated in the shole range of the buffer and cells for class 1 are allocated up to discard threshold of the buffer. In case cells in the buffer are transmitted, one cell for class 1 is transmitted whenever the maximum K cells for class 2 are transmitted consecutively. We analyze the time delay and the loss probability for each class of traffic using Markov chain. The results show that the characteristics of the mean cell delay about cells for class 1 becomes better and that of the cell loss probability about cells for class 2 becomes better by selecting properly discard threshold of the buffer and the cell transfer ratio according to the condition of input traffic.