This paper proposes a fast access scheme to meet delay requirement for the wireless Medium Access Control (MAC) protocols to support the Quality of Service (QoS) requirements of real-time applications. Our scheme deals with access requests in different ways depending on their delay requirements. In our scheme, a Collision Resolution Period (CRP) is used to quickly resolve collisions for the delay sensitive traffic in order to support their delay requirements. Performance analysis and simulation results show that our scheme may successfully meet the delay requirements of real time applications by reducing access delays and collisions.