As the technology of multimedia applications in Wireless Sensor Networks (WSNs) is highly desired nowadays, how to guarantee real-time service becomes one of the biggest research challenges in this area. Even though lots of related works have been conducted to meet this requirement in several ways, the specific traffic model for multimedia applications has not been taken yet. It makes these new approaches not adaptable in real deployments. To solve this problem, in this paper, we model the real-time streams of multimedia applications with (m,k)-firm guarantee, using the firm real-time property it contains. A local transmission status indicator modified based on stream DBP (Distance-Based Priority), called L_DBP (local-DBP), is used to monitor the statement of delivery to the next hop and indicate network faults such as congestion and link failure during transmissions. By the contributions of both L_DBP and stream DBP, a novel geographic routing protocol is proposed to meet the requirements of real-time streams, by making routing decisions while considering timeliness and reliability features together. Simulation results reveal that (m,k)-firm is a good traffic model for multimedia sensor networks and the proposed routing protocol can efficiently avoid stream end-to-end dynamic failure, which is considered to be the main reason of QoS performance degradation.