Distributed data centers are considered very important for data storage services in the contemporary computing world especially with the increased amount of data that are needed to be stored and retrieved. Data retrieval speed performance is a sensitive issue when considering the huge amount of data that need to be retrieved from several nodes over the network. Data prefetch has proved to be an important technique for reducing data reading time from the distributed nodes. In such distributed environment, data fetching time from a node to an another consists of the disk reading time and the network transmission time. Multi-layer (hybrid) storage provides high performance solutions for big data centers. We introduce a solution PPDHSS that implements predictive-probability graph to predictively prefetch the data that are expected to be accessed by the application in the near future from the lower level hard disk of the storage-side nodes (slower) to the top level solid state disk (faster) in parallel which the application data reading requests that comes from the client-side node by taking advantage of the storage system's parallelism. Our performance evaluation in which we used real traces shows that our system can reduce the data fetching time from storage side-nodes to the client-side nodes without the need of using caches of large size.