The problem of session-aware recommendation aims to predict users’ next click based on their current session and historical sessions. Existing session-aware recommendation methods have defects in capturing complex item transition relationships. Other than that, most of them fail to explicitly distinguish the effects of different historical sessions on the current session. To this end, we propose a novel method, named Personalized Graph Neural Networks with Attention Mechanism (A-PGNN) for brevity. A-PGNN mainly consists of two components: one is Personalized Graph Neural Network (PGNN), which is used to extract the personalized structural information in each user behavior graph, compared with the traditional Graph Neural Network (GNN) model, which considers the role of the user when the node embedding is updated. The other is Dot-Product Attention mechanism, which draws on the Transformer net to explicitly model the effect of historical sessions on the current session. Extensive experiments conducted on two real-world data sets show that A-PGNN evidently outperforms the state-of-the-art personalized session-aware recommendation methods.