During peer evaluation, evaluators may give inaccurate evaluation scores as a result of strategic evaluation. Taking into account the evaluators’ social interest (SI) relations, this study proposes a prediction method named graph attention network-social interest relation-oriented attention network (GAT-SIROAN) that integrates SI and the GAT. This method consists of a weighted network SIROAN that represents the evaluators’ relations with the solutions and a GAT that is used to predict peer evaluation scores. In the SIROAN, the interrupted time-series analysis (ITSA) method is applied to define the evaluators’ two characteristics: the self-evaluation ability and the peer evaluation ability, and these two characteristics are compared to obtain the SI factors and relations among the evaluators. In the score prediction stage, considering the importance of each node, this study uses a self-attention mechanism to calculate the attention coefficients at the nodes, thereby improving the prediction ability. Network parameters are learned by minimizing the root mean square error (RMSE) to obtain more accurate predicted peer evaluation scores. The GAT-SIROAN method is compared experimentally with five baseline methods, namely, the mean, median, PeerRank, RankwithTA, and GCN-SOAN methods, on real datasets. The results show that the GAT-SIROAN method outperforms all the above baseline methods in the RMSE.