Identification of essential proteins is key to understanding the minimal requirements for cellular life and important for drug design. The rapid increase of available protein-protein interaction (PPI) data has made it possible to detect protein essentiality on network level. A series of centrality measures have been proposed to discover essential proteins based on network topology. However, most of them tended to focus only on the location of single protein, but ignored the relevance between interactions and protein essentiality. In this paper, a new centrality measure for identifying essential proteins based on edge clustering coefficient, named as NC, is proposed. Different from previous centrality measures, NC considers both the centrality of a node and the relationship between it and its neighbors. For each interaction in the network, we calculate its edge clustering coefficient. A node’s essentiality is determined by the sum of the edge clustering coefficients of interactions connecting it and its neighbors. The new centrality measure NC takes into account the modular nature of protein essentiality. NC is applied to three different types of yeast protein-protein interaction networks, which are obtained from the DIP database, the MIPS database and the BioGRID database, respectively. The experimental results on the three different networks show that the number of essential proteins discovered by NC universally exceeds that discovered by the six other centrality measures: DC, BC, CC, SC, EC, and IC. Moreover, the essential proteins discovered by NC show significant cluster effect.