Essential proteins have extremely important role in disease diagnosis and drug development. Many methods have been devoted to the essential protein prediction by using some kinds of biological information. However, they either ignore the noise presented in the biological information itself or the noise generated during feature extraction. To overcome these problems, in this paper, we propose a novel method for predicting essential proteins called AG-GATCN. In AG-GATCN method, we use improved temporal convolutional network (TCN) to extract features from gene expression sequence. To address the noise in the gene expression sequence itself and the noise generated after the dilated causal convolution, we introduce attention mechanism and gating mechanism in TCN. In addition, we use graph attention network (GAT) to extract protein-protein interaction (PPI) network features, in which we construct the feature matrix by introducing node2vec technique and 7 centrality metrics, and to solve the GAT oversmoothing problem, we introduce Gated Tanh Unit (GTU) units in GAT. Finally, two types of features were integrated by us to predict essential protein. Compared with the existing methods for predicting essential proteins, the experimental results show that AG-GATCN achieves better performance.