Many wireless sensor network (WSN) applications require real-time communication. One of the most important and challenging issues in real-time applications of resource-constrained WSNs is providing end-to-end delay requirement. To address such an issue a few QoS routing protocols have been proposed. Also, in many applications, the delay level required by the data packets is different. In this paper, we focus on building an energy-efficient real-time routing protocol called EERT which routes the differentiated classified packets towards the destination node via a modular approach. It takes into account both power transmission costs and residual energy of routers along with nearness of node to the shortest path and link usage in the energy-efficient module in order to prolong the network life time. Moreover, EERT employs a new policy called re-routing policy which allows the packets of a specific class to be routed as the packets of a lower/higher real-time class in particular situations. In this way, it can improve real-time performance by means of reducing the packet dropping in routing decisions.