This paper proposes a new scheduling algorithm named TWFQ (Two-phased Weighted Fair Queueing) not only to maintain the fair utilization of available bandwidth but also to improve the performance of CDV and cell loss probability. The TWFQ algorithm makes use of the cell inter-arrival time of each connection for determining the cell service order among connections, which contributes to get a small CDV. To achieve low cell loss probability, the TWFQ allows connections, which suffer from the more bursty input traffic, to send the cell with more opportunities by using two scheduling phases. Through simulations, we show that the proposed algorithm achieves good performance in terms of CDV and cell loss probability, while other performance criteria are preserved in an acceptable level.