CDN (Content Delivery Networks) improves end-user performance by replicating web contents on a group of geographically distributed servers. However, repeatedly keeping the entire replica of the original objects into many content servers consumes too much server resource. This problem becomes more serious for the large-sized objects such as streaming media, e.g. high quality video. In this paper, we therefore propose an efficient replication method for layered video streams in CDN, which can reduce user response delays and storage costs simultaneously. Based on an analytical formulation of the cooperative replication of layers and segments of each video stream, we derive a replication algorithm which solves next three problems quantitatively. (1) How many servers should be selected to replicate a given video stream? (2) For a single video stream, how many layers and segments should be stored in a given server? (3) After selecting a group of servers for each video stream, how do we allocate the replication priority (i.e. order) to each server? Simulation results verify that the proposed algorithm efficiently resolves the above problems and provides much better performance than conventional methods.