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As important side information, attributes have been widely exploited in the existing recommender system for better performance. In the real-world scenarios, it is common that some attributes of items/users are missing (e.g., some movies miss the genre data). Prior studies usually use a default value (i.e., "other") to represent the missing attribute, resulting in sub-optimal performance. To address this problem, in this paper, we present an attribute-aware attentive graph convolution network (A${^2}$-GCN). In particular, we first construct a graph, whereby users, items, and attributes are three types of nodes and their associations are edges. Thereafter, we leverage the graph convolution network to characterize the complicated interactions among <users, items, attributes>. To learn the node representation, we turn to the message-passing strategy to aggregate the message passed from the other directly linked types of nodes (e.g., a user or an attribute). To this end, we are capable of incorporating associate attributes to strengthen the user and item representations, and thus naturally solve the attribute missing problem. Considering the fact that for different users, the attributes of an item have different influence on their preference for this item, we design a novel attention mechanism to filter the message passed from an item to a target user by considering the attribute information. Extensive experiments have been conducted on several publicly accessible datasets to justify our model. Results show that our model outperforms several state-of-the-art methods and demonstrate the effectiveness of our attention method.