Organizing　user-item　interaction　data　into　a　graph　has　brought　many　benefits　to　recommendation　methods.　Compared　with　the　user-item　bipartite　graph　structure,　a　hypergraph　structure　provides　a　natural　way　to　directly　model　high-order　correlations　among　users　or　items.　Hypergraph　Convolution　Network　(HGCN)　has　the　capability　of　aggregating　and　propagating　latent　features　of　nodes　in　the　hypergraph　nonlinearly.　Recently,　recommendation　models　based　on　simplified　HGCN　have　shown　good　performance.　However,　such　models　lose　the　powerful　expression　ability　of　feature　crossing　and　suffer　from　limited　labeled　data.　To　tackle　these　two　problems,　a　framework　called　HGCN-CC　is　proposed　to　improve　HGCN　with　feature　Crossing　and　Contrastive　learning.　Specifically,　HGCN　is　combined　with　a　feature　cross　network　in　a　parallel　manner　to　balance　between　feature　crossing　and　over　smoothing.　By　such　a　design,　HGCN-CC　not　only　utilizes　simplified　propagation　operation　in　HGCN　to　capture　high-order　correlations　among　users　or　items,　but　also　enjoys　the　powerful　expressing　ability　of　high-order　feature　interactions.　Furthermore,　HGCN-CC　resorts　to　contrastive　learning　to　help　learn　good　representations.　Under　the　HGCN-CC　framework,　two　models　called　item-based　HGCN-CC　(I-HGCN-CC)　and　user-based　HGCN-CC　(U-HGCN-CC)　are　constructed　to　emphasize　different　aspects　of　data.　Results　of　extensive　experiments　on　four　benchmark　datasets　demonstrate　that　proposed　models　have　superiority　in　modelling　hypergraph　structure　data　for　recommendations.