Under the combined effects of global data scaling, integration and frontiers, as well as the derivative impact of COVID-19, it is difficult to timely and effectively complete cross-border data evidences collection through traditional bilateral law enforcement cooperation and judicial assistance. Unilateral controlling schemes, such as EU framework based on a package plan or US framework based on Cloud Act and its derivative agreements, cannot prevent the functional imbalance of governing cross-border data evidence collection. It is urgent to combine specific characteristics of data evidence in information society, improve multilateral rules for governing cross-border data evidences collection in a targeted manner, and gradually build a unified, coordinated, and well regulated governance mechanism, consolidate cooperation based on common interests, emphasize the extraterritorial application of legislation within the domain, restrict the specific application of cross-border data evidences collection, and adhere to the governance model of legitimate collection of cross-border data evidences, effectively safeguard data sovereignty, social security and legitimate rights and interests of different entities, and promote the healthy and orderly development of digital economy.