Emergency communication systems play a major role in disaster-relief environments. In terms of the public safety research, the emergency relief communication system can provide a high system capacity for networks based on the development of Long-Term Evolution. However, in the event of a disaster, mass traffic information can cause congestion in the core network, and communications between relief workers may be limited. Consequently, spectrum efficiency can be very weak. This paper provides a hybrid traffic offloading mechanism combining Device-to-Device (D2D) and Local IP Access (LIPA) modes for the disaster-resilient network. With receiving power, the distance between relief workers and the distance between relief workers and the vehicular eNodeB (VeNB) as the LIPA/D2D switching criteria, the network can select an appropriate mode to prevent core network congestion. This paper also considers the effects of the mobility models (i.e., random walk and random direction) on the spectrum efficiency of the disaster-resilient communication system. The proposed hybrid LIPA/D2D traffic offloading mechanism can prevent the local communication traffic from flowing into the core network and significantly improve the system spectrum efficiency when the core network is under congestion. Therefore, the proposed mechanism can effectively improve the quality of the communication between relief workers served by the same VeNB for performing rescue operations. Moreover, the hybrid LIPA/D2D traffic offloading mechanism can be applied to the smart city and smart home in the future.