In this paper, we proposed and analysed two kinds of priority control mechanism to archive the cell loss rate requirement and the delay requirement of each class. The service classes of our concern are the high time priority class(class 1) and the high loss priority class(class 2). Two kinds of priority control mechanism is divided by the method of storing the arriving class 2 cell in buffer on case of buffer full. The first one is the method which discarding the arriving class 2 cell, the second one is the mothod which storing the arriving class 2 cell on behalf of pushing out the class 1 cell in buffer. In the proposed priority schemes, one cell of the class 1 is transmitted whenever the maximum K cells of the class 2 is transmitted on case of transmitting the class 1 cell and the class 2 cell sequentially. In this paper, we analysed the cell loss rate and the mean cell delay for each class of the proposed priority scheme by using the Markov chain. The analytical results show that the characteristic of the mean cell delay becomes better for the class 1 cell and that of the cell loss rate becomes better for the class 2 cell by selecting properly the cell transfer ratio according to the condition of input traffic.