The IEEE 802.11 MAC (Media Access Control) Protocol supports two modes of operation, a random access mode for non-real-time data applications served by Distributed Coordinated Function (DCF), and a polling mode for real-time applications served by Point Coordinated Function (PCF). It is known that the standard IEEE 802.11 scheme is insufficient to serve real-time traffic. For providing Quality of Service (QoS) of real-time traffic, we propose the Down-First Scheduling scheme with Earliest Due Date (EDD) in Contention Free Period (CFP) and admission control. We analyze the capacity and deadline violation of two systems. Though the effect of piggybacking in proposed system is less than that of standard system, the difference is so small and can be neglected. With computation and simulation results, we verify that the proposed scheme is remarkably efficient at the deadline violation probability. At the cost of blocking probability, the proposed system provides QoS of real-time traffic services