Wireless sensor networks (WSNs) are formed by a great quantity of sensor nodes, which are consisted of battery-powered and some tiny devices. In WSN, both efficient energy management and Quality of Service (QoS) are important issues for some applications. Real-time services are usually employed to satisfy QoS requirements in critical environment. This paper proposes a real-time MAC (Medium Access Control) protocol with extended backoff scheme for wireless sensor networks. The basic idea of the proposed protocol employs (m,k)-firm constraint scheduling which is to adjust the contention window (CW) around the optimal value for decreasing the dynamic failure and reducing collisions DBP (Distant Based Priority). In the proposed protocol, the scheduling algorithm dynamically assigns uniform transmitting opportunities to each node. Numerical results reveal the effect of the proposed backoff mechanism.