© 2018, Springer Nature B.V. As data source for Big Data, wireless sensor networks play great role in data collection and dissemination. Specially, real-time communication remains one of the crucial research challenges, because of the high complexity and severe networking requirements on restrained node in wireless sensor networks. Moreover, current schemes are assumed to take general traffic model for real-time delivery so they lack adaptability. To solve this problem, few routing protocols have been designed to accommodate new real-time model, (m,k)-firm, which is regarded as the most applicable scheme for event as well as query based applications in wireless sensor networks. However, since current schemes for (m,k)-firm stream are proposed to support unicast communications only, they cannot be applied to multicast communications where many group members are willing to receive data packets from the sink node. To overcome this problem, we propose a new multicast scheme for (m,k)-firm stream to deliver data packet to group members. To construct a multicast tree, different types of overlay tree are constructed according to distance based priority (DBP) value. Simulation results prove that the proposed scheme can meet (m,k)-firm requirement and have longer network lifetime than existing schemes.