With the explosive growth of Web traffic, the load on a Web server becomes heavier, leading to the longer user-perceived latency. Website operators would like to employ service differentiation to offer better throughput and shorter user-perceived latency to some specific users. This paper presents an HTTP request scheduling algorithm deployed at the website gateway to enable the Web quality of service without any modification to client or server software. A variation of the deficit round robin scheduling algorithm and a window control mechanism are presented to decide the order and the releasing time of requests, respectively. The order is decided by the response size of the requests and the pre-defined service weights. The ratio of the bandwidth throughput of the service classes is determined by the weights, whereas the releasing time is decided by the service rate of the Web server. The evaluation reveals the scheduling algorithm can provide service differentiation and improve server throughput and user-perceived latency.