Collaborative　filtering　with　large　amount　of　user　data　will　raise　serious　risk　privacy　of　individuals.　How　to　protect　private　data　information　from　disclosure　has　become　one　of　the　greatest　challenges　to　recommender　systems.　Differential　privacy　has　emerged　as　a　new　paradigm　for　privacy　protection　with　strong　privacy　guarantees　against　adversaries　with　arbitrary　background　knowledge.　Although　several　studies　explored　privacy-enhanced　neighborhood-based　recommendations,　little　attention　has　been　paid　to　privacy　preserving　latent　factor　models.　To　address　the　problem　of　privacy　preserving　in　recommendation　systems,　a　new　collaborative　filtering　recommendation　algorithm　based　on　differential　privacy　is　proposed　in　this　paper,　which　achieves　trade-off　between　recommendation　accuracy　and　privacy　by　matrix　factorization　technique.　Firstly,　user　and　item　latent　feature　matrices　are　constructed　for　decreasing　sparsity.　After　that,　matrix　factorization　model　with　noise　is　generated　by　adding　the　differential　noisy　using　objective　perturbation　method,　and　then　stochastic　gradient　descent　is　utilized　to　minimize　regularized　squared　error　function　and　learn　the　parameters　of　model.　Finally,　we　apply　a　differentially　private　matrix　factorization　model　to　predict　the　ratings　and　conduct　experiments　on　the　MovieLens　and　Netflix　datasets　to　evaluate　its　effectiveness.　The　experimental　results　demonstrate　that　our　proposal　is　efficient　and　has　limited　side　effects　on　the　precision　of　recommendation.　©　2017,　Science　Press.　All　right　reserved.