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Network tomography is a newly developing technology for network administrators to monitor, predict and diagnose their networks, which is applied to infer network internal parameters with end-to-end measurement under no participant and no help of internal network elements. Delay is one of important parameter in network internal performances, so the measure of delay performance is very necessary. The up-to-date algorithms on delay tomography are mainly Maximum Likelihood Estimate (MLE) and EM-MLE (Expectation Maximum) algorithm, but it is complex in their computation, especially when the size of network topology is large. So the method of moment was proposed to infer the delay performance of internal network. In contrast to other methods, it is simple in the computational complexity using the method of moment but its accuracy is not high. In this paper, an improvement is made on the method of moment, which tries to get higher accuracy in delay distribution inference.