As one of the workload characteristics, the anomaly behaviorsin real workload have been recognized as a critical requirement for file system design. In this paper, a set of traces collected from typically realistic file system have been analyzed. Studying the correlations of I/O request inter-arrival times shows that it is necessary to examine the self-similarity in file system workload. And then the phenomenon of self-similarity which had been initially observed in network and disk I/O workload has also been visually and statistically observed in file system workload used in this paper. Furthermore, this property is further explored and we find that the self-similarity of I/O accesses in those sets of traces studied in this paper is mainly due to reads. This study is extremely important to provide useful insight into the design and analysis of file system for performance gains, as well as to model file system I/O workloads.