There have been increasing interests in studying multiplex dynamical networks recently. This paper focuses on topology identification of two-layer multiplex networks with peer-to-peer interlayer couplings. For a two-layer network model in which different layers have different coupling patterns, we propose novel methods to recover unknown topological structure of one layer, using the information of the other layer known as a prior. The proposed methods make full use of the measured evolutional states of the multiplex network itself, and treat the layer with a known structure as an auxiliary layer which is designed to identify the unknown topological layer. Compared with the traditional synchronization-based identification method, the proposed methods are in no need of constructing an additional auxiliary network to identify the unknown topological layer, and thus greatly reduce the cost of topology identification. Finally, numerical simulations validate the effectiveness of the proposed methods.