One of the challenges that businesses have always paid more attention to is supply chain logistics competence. The conditions of supply chain logistics capabilities management have also altered in light of the quick development of multimedia, and there will undoubtedly be certain management issues. Logistics competence is expressed in both real and intangible capabilities in the context of the supply chain. As a result, this paper presents research on supply chain logistics capability management strategy based on the distributed platform under the multimedia background, elaborates on the supply chain logistics capability optimization standard under the multimedia background, analyzes the impact of multimedia background on supply chain logistics capability management, establishes a new type of supply chain relationship and strengthens the judgment of enterprise market information. This study concludes by proposing measures for supply chain logistics capability management, such as enhancing the infrastructure for supply chain logistics capability management and strengthening supplier management. The experimental findings demonstrate that we can effectively increase the supply chain’s supply efficiency, achieve a 13% performance improvement and reduce the cost of the supply chain by using the logistics framework in a distributed environment.