The clustering of nodes is an important feature of complex network. Previous researches mainly focus on community discovery in unweighted network, with little attention paid to the weighted network because of the complexity of weighted network. The community discovery of the weighted network is believed to be a much more difficult task. In this paper, we perform a study on the effectivenesses of community evaluation criterion and the performances of the existing discovery algorithms. First, we summarize three classical community evaluation criterions of weighted network, and analyze their effectivenesses according to a simulated noisy dataset, which has different community sizes, densities and local characteristics. Second, we adopt five datasets to compare the performances of three typical community discovery algorithms. The study shows that the existing criterions encounter difficulties in evaluating the basic community structure and in evaluating the weighted community with complex structure, and the generalization ability of the typical community discovery algorithm of weighted network is unsatisfactory.