<p>Complex networks can analyze various phenomena within complex systems, and the global exchange-rate market is a prime example of such a complex system. With the daily closing exchange-rates from China, the U.S., and ASEAN countries, this paper investigates the influence of the RMB and USD on the ASEAN exchange-rate market. Using distribution-free overlapping index, a two-layer exchange-rate network is constructed, where log-returns sections are regarded as the nodes. To eliminate noise in the network newly achieved, we propose a new threshold index, named network-structure-change rate, to obtain an optimal two-layer network. Further, a novel key-nodes identification algorithm via weighted-degree and dispersion-degree, called WDB-KN-I algorithm is put forward. Compared with PageRank, this algorithm is better for identifying stable key log-returns sections. Applying this algorithm, we conclude that the USD exerts a more significant influence on the ASEAN exchange-rate market than the RMB during certain periods, notably affecting the Vietnamese Dong, Cambodian Riel, Brunei Dollar, and Philippine Peso.</p>