Collaborative　filtering　is　the　most　popular　and　successful　information　recommendation　technique.　However,　it　can　suffer　from　data　sparsity　issue　in　cases　where　the　systems　do　not　have　sufficient　domain　information.　Transfer　learning,　which　enables　information　to　be　transferred　from　source　domains　to　target　domain,　presents　an　unprecedented　opportunity　to　alleviate　this　issue.　A　few　recent　works　focus　on　transferring　user-item　rating　information　from　a　dense　domain　to　a　sparse　target　domain,　while　almost　all　methods　need　that　each　rating　matrix　in　source　domain　to　be　extracted　should　be　complete.　To　address　this　issue,　in　this　paper　we　propose　a　novel　multiple　incomplete　domains　transfer　learning　model　for　cross-domain　collaborative　filtering.　The　transfer　learning　process　consists　of　two　steps.　First,　the　user-item　ratings　information　in　incomplete　source　domains　are　compressed　into　multiple　informative　compact　cluster-level　matrixes,　which　are　referred　as　codebooks.　Second,　we　reconstruct　the　target　matrix　based　on　the　codebooks.　Specifically,　for　the　purpose　of　maximizing　the　knowledge　transfer,　we　design　a　new　algorithm　to　learn　the　rating　knowledge　efficiently　from　multiple　incomplete　domains.　Extensive　experiments　on　real　datasets　demonstrate　that　our　proposed　approach　significantly　outperforms　existing　methods.