Aiming　at　the　problem　of　sparse　data　and　user　cold　start　in　a　single　domain　for　collaborative　filtering,　this　paper　proposes　a　cross-domain　recommendation　model　called　cross-domain　variational　autoencoder　(CDVAE)　based　on　Bayesian　theory.　The　model　uses　rating　data　to　construct　latent　representations　of　users　and　items　in　multiple　domains,　utilizes　overlapping　users　in　different　domains,　and　draws　on　the　idea　of　variational　autoencoder　(VAE)　to　train　a　user　generating　networks　cross-domains　based　on　user　preferences　to　different　domains.　Bayesian　theory　is　introduced　to　ensure　the　generation　ability　and　robustness　of　the　model.　Finally,　based　on　the　user＇s　preference　to　the　source　domain,　the　user＇s　preference　prediction　in　the　target　domain　is　obtained.　The　generation　of　the　recommendation　result　is　obtained　by　the　user＇s　preference　weighting　in　the　source　domain　and　the　target　domain,　and　the　user＇s　multi-source　interest　preference　is　considered　to　improve　the　accuracy.　The　experimental　results　show　that　CDVAE　is　able　to　significantly　outperform　the　state-of-the-art　recommendation　methods　of　more　robust　performance.　©　2019　IEEE.