Session-based recommendation (SBR) aims to predict the user’s action at the next timestamp according to an anonymous yet short interaction sequence (i.e., session). Almost all the existing SBR solutions for user preference are only based on the current session without exploiting the high-order relations among other sessions, which may restrict the SBR representation ability and even deteriorate the performance. To this end, we propose a Hyper-relation alignment hyperGraph Convolutional Network, called Hyra-GCN, for better inferring the user preference of the current session. Specifically, we first model session-based data as a hyper-graph capable of representing high-order relationships to exploit item transitions over sessions in a more subtle manner. Subsequently, we explore self-supervised learning on item-session hypergraphs, so as to alleviate the problem of data sparsity. Experimental results on real-world datasets demonstrate the effectiveness of our proposed Hyra-GCN against state-of-the-art baselines.