We propose the conception and evaluation indexes of emergency logistics network connecting reliability to construct evaluation index system of complex network reliability, and describe these indexes quantitatively to evaluate the network connecting reliability. Moreover, the network topological model and the simulation methods of reliability measurement when the network is under attack are present. Finally, we take three classical emergency logistics networks as examples, and through emulation analysis we obtain the connecting reliability changing situation of these three networks under random attack, the changing curve of the ratio of effective demand nodes and emergence supply mileage of emergency logistics network with same network density but different forms, and then evaluate the emergency logistics network connecting reliability. This can provide references for the designing of emergency logistics network with high reliability and analysis means for research in other fields.