Identifying essential proteins is very important for understanding the minimal requirements of cellular survival and development. Fast growth in the amount of available protein-protein interactions has produced unprecedented opportunities for detecting protein essentiality on network level. A series of centrality measures have been proposed to discover essential proteins based on network topology. Unfortunately, the protein-protein interactions produced by high-throughput experiments generally have high false positives. Moreover, most of centrality measures based on network topology are sensitive to false positives. We therefore propose a new method for evaluating the confidence of each interaction based on the combination of logistic regression-based model and function similarity. Nine standard centrality measures in weighted network were redefined in this paper. The experimental results on a yeast protein interaction network shows that the weighting method improved the performance of centrality measures considerably. More essential proteins were discovered by the weighted centrality measures than by the original centrality measures used in the unweighted network. Even about 20% improvements were obtained from closeness centrality and subgraph centrality.