Session-based recommendation(SBR) aims to provide more accurate recommendations to users based on anonymous behavior sequences. Almost all the existing graph neural networks for SBR models only focus on converting session sequences into a single type of graph, which can not provide effective and comprehensive item transformation relationships to improve the performance of capturing user preferences. In this paper, we propose a Hypergraph Reinforced Graph Collaborative Learning (HGL-SR) to compensate for the shortcomings of a single type in graph modeling. HGL-SR learns two levels of item embeddings from session graphs and hypergraphs. Specifically, we design a session graph channel and a hypergraph channel. In the session graph channel, we capture the low-order transition information of items using the contextual relationships in the session sequence. And for cross-session potential sequence aspects, we view each session as a collection of items, construct hypergraphs and learn higher-order transition information between items. To make the hypergraph learning results better for reinforcing session graph learning, we design a collaborative learning module to capture more accurate user preferences through item information. Extensive experiments conducted on two real datasets show that HGL-SR outperforms the state-of-the-art session-based recommendation methods consistently.