Traffic matrix (TM) describes the traffic volumes traversing a network from the input nodes to the output nodes over a measured period. Such a TM contains very useful information for network managers, traffic engineers and users. However, TM is hard to be obtained and analyzed due to its large size, especially for large-scale networks. In this paper, we present a new method based on diffusion wavelets for analyzing the traffic matrix. It is shown that this method can conduct efficient multi-resolution analysis (MRA) on TM. We compare the analysis results by using different diffusion operators. Through reconstructing the original TM from the diffused traffic on a particular level, we show the high efficiency of this MRA tool based on these operators. We then develop an anomaly detection method based on the analysis results and explore the possibilities of other potential applications.