In this paper, the design of a QoS scheduling scheme for the Internet traffic is proposed by considering the correlation property of the arriving traffic. The basic concept of the Weighted Fair Queuing (WFQ) is adopted in the proposed scheme, however, the correlation property of the traffic stream is applied as the heuristic to adjust the share weight factors of each traffic type dynamically. The Auto Regressive Integrated Moving Average (ARIMA) model is applied in this paper to characterize the correlation property of the Internet traffic. And the share weight factors are derived from the parameters of the AR part and MA part. Experimental simulations are performed to illustrate the effectiveness of the proposed scheme. In addition to comparing the performance of each service types, we also define a fair play parameter (FPP) to examine the fairness index among various traffic streams of the proposed scheme. The experimental results indicate that the proposed scheme demonstrates a quite good performance in scheduling the integrated services and the fairness among service classes can also be achieved, especially when the link capacity is limited.