Essential proteins are vital for an organism's viability under a variety of conditions. There are many experimental and computational methods developed to identify essential proteins. Computational prediction of essential proteins based on the global protein-protein interaction (PPI) network is severely restricted because of the insufficiency of the PPI data, but fortunately the gene expression profiles help to make up the deficiency. In this work, Pearson correlation coefficient (PCC) is used to bridge the gap between PPI and gene expression data. Based on PCC and edge clustering coefficient (ECC), a new centrality measure, i.e., the weighted degree centrality (WDC), is developed to achieve the reliable prediction of essential proteins. WDC is employed to identify essential proteins in the yeast PPI and e-Coli networks in order to estimate its performance. For comparison, other prediction technologies are also performed to identify essential proteins. Some evaluation methods are used to analyze the results from various prediction approaches. The prediction results and comparative analyses are shown in the paper. Furthermore, the parameter λ in the method WDC will be analyzed in detail and an optimal λ value will be found. Based on the optimal λ value, the differentiation of WDC and another prediction method PeC is discussed. The analyses prove that WDC outperforms other methods including DC, BC, CC, SC, EC, IC, NC, and PeC. At the same time, the analyses also mean that it is an effective way to predict essential proteins by means of integrating different data sources.