Cobalt and lithium are important strategic metal materials. At present, most countries' demand for cobalt and lithium mainly comes from international trade. To a certain extent, they are joint consumption, and the demand for lithium and cobalt in various countries has shown synergistic changes. In order to explore the complex relationship between cobalt trade and lithium trade, as well as the impact of low-cobalt technology development trends on the crucial metal of lithium batteries, this paper builds the multiplex cobalt-lithium trade network (CLTN) based on the global cobalt trade network and the global lithium trade network. We review the evolution of trade pattern of CLTN from 2010 to 2019, and explore the correlation between cobalt trade layer and lithium trade layer. Furthermore, the impacts of low-cobalt technology for lithium batteries on the CLTN are quantitatively analyzed. The results show that the globalization trend of CLTN is becoming more and more obvious, and the relationship between cobalt trade and lithium trade is getting closer. With the increasing shock of low-cobalt technology, the impact of the cobalt trade layer affected by technology on the lithium trade layer has become more and more obvious. Finally, some policy implications are provided for regulators to reduce trade risks.