Docker, as a mainstream container solution, adopts the Copy-on-Write (CoW) mechanism in its storage drivers. This mechanism satisfies the need of different containers to share the same image. However, when a single container performs operations such as modification of an image file, a duplicate is created in the upper read-write layer, which contributes to the runtime overhead. When the accessed image file is fairly large, this additional overhead becomes non-negligible. Here we present the concept of Dynamic Prefetching Strategy Optimization (DPSO), which optimizes the CoW mechanism for a Docker container on the basis of the dynamic prefetching strategy. At the beginning of the container life cycle, DPSO pre-copies up the image files that are most likely to be copied up later to eliminate the overhead caused by performing this operation during application runtime. The experimental results show that DPSO has an average prefetch accuracy of greater than 78% in complex scenarios and could effectively eliminate the overhead caused by the CoW mechanism.