An efficient, accurate and distributed metadataoriented prefetching scheme is critical to the overall performance in large distributed storage systems. In this paper, we present a novel weighted-graph-based prefetching technique, built on successor relationship, to gain performance benefit from prefetching specifically for clustered metadata servers, an arrangement envisioned necessary for petabyte-scale distributed storage systems. Extensive trace-driven simulations show that by adopting our new prefetching algorithm, the hit rate for metadata access on the client site can be increased by up to 13%, while the average response time of metadata operations can be reduced by up to 67%, compared with LRU and an existing state of the art prefetching algorithm.