Intra　prediction　plays　an　important　role　in　reducing　the　spatial　redundancy　for　intra　frame　encoding　in　H.264/AVC.　In　this　paper,　we　propose　a　low-rank　matrix　completion　based　intra　prediction　to　improve　the　prediction　efficiency.　According　to　the　low-rank　matrix　completion　theory,　a　low-rank　matrix　can　be　exactly　recovered　from　quite　limited　samples　with　high　probability　under　mild　conditions.　After　moderate　rearrangement　and　organization,　image　blocks　can　be　represented　as　low-rank　or　approximately　low-rank　matrix.　The　intra　prediction　can　then　be　formulated　as　a　matrix　completion　problem,　thus　the　unknown　pixels　can　be　inferred　from　limited　samples　with　very　high　accuracy.　Specifically,　we　novelly　rearrange　the　encoded　blocks　similar　to　the　current　block　to　generate　an　observation　matrix,　from　which　the　prediction　can　be　obtained　by　solving　a　low-rank　minimization　problem.　Experimental　results　demonstrate　that　the　proposed　scheme　can　achieve　averagely　5.39%　bit-rate　saving　for　CIF　sequences　and　4.21%　for　QCIF　sequences　compared　with　standard　H.264/AVC.