Effective call admission control is desirable to control an ATM traffics. It should provide high fairness and utilization for different kinds of services during call admission. Complete bandwidth sharing method is efficient for utilization of bandwidth but not efficient for fairness of call admission. Complete bandwidth partitioning method is efficient for fairness but not efficient for utilization. We propose a new CST(Complete Sharing with Threshold) algorithm using threshold on a total link to improve fairness and utilization.