Despite the increasing attention of multiplex networks in recent years, topology identification of the network is challenging. This brief addresses the problem of topology identification of multiplex delayed network, where each layer has its own time delay. An algorithm for identifying the topologies of all the layers and the system parameters of the nodes is proposed. A duplex network is provided to validate the effectiveness of the theoretical results. Numerical results show that the inner couplings and the time delays have significant impact on topology identification. With the fixed inner couplings (time delay) of one layer, the logarithmic growth of other layer’s inner couplings (time delay) in a certain range is beneficial to the identification performance.