The identification of key nodes in complex network plays an important role in the optimization of network structure and effective propagation of information. Local structural Entropy （LE） can be used to identify key nodes by using the influence of the local network on the whole network instead of the influence of nodes on the whole network. However， the cases of the highly aggregative network and nodes forming a loop with neighbor nodes are not considered in LE， which leads to some limitations. To address these limitations， firstly， an improved LE based node importance evaluation method， namely PLE （Penalized Local structural Entropy）， was proposed， in which based on the LE， the Clustering Coefficient （CC） was introduced as a penalty term to penalize the highly aggregative nodes in the network appropriately. Secondly， due to the fact that the penalty of PLE penalizing the nodes in triadic closure structure is too much， an improved method of PLE， namely PLEA （Penalized Local structural Entropy Advancement） was proposed， in which control coefficient was introduced in front of the penalty term to control the penalty strength. Selective attack experiments on five real networks with different sizes were conducted. Experimental results show that in the western US states grid and the US Airlines， PLEA has the identification accuracy improved by 26.3% and 3.2% compared with LE respectively， by 380% and 5.43% compared with K-Shell （KS） method respectively， and by 14.4% and 24% compared with DCL （Degree and Clustering coefficient and Location） method respectively. The key nodes identified by PLEA can cause more damage to the network， verifying the rationality of introducing the CC as a penalty term， and the effectiveness and superiority of PLEA. The integration of the number of neighbors and the local network structure of nodes with the simplicity of computation makes it more effective in describing the reliability and invulnerability of large-scale networks.