The interaction between entities in complex systems is vividly described by multiplex networks， and motifs frequently appear in networks as a higher-order structure. Compared with single-layer motifs， multiplex motifs have the characteristics of large quantity， diverse types， and complicated structure. Given the current lack of complete detection algorithm for multiplex motifs， a Fast Algorithm for Multiplex Motif Detection （FAMMD） suitable for multiplex networks was proposed. Firstly， an improved ESU （Enumerate SUbgraphs） algorithm was used to enumerate multiplex subgraphs. Then a method combining layer markers and binary strings was used for accelerating the process of isomorphism detection， and a null model that preserved degree sequences and inter-layer dependencies was constructed for multiplex subgraph testing. Finally， motif detection was performed on two-layer real networks. Multiplex motifs exhibited a closely connected triple mode， and they were more homogeneous in social networks while more complementary in transportation networks. Experimental results show that the proposed method can accurately and quickly detect multiplex motifs that reflect the structure characteristics of the network and conform the actual situation.