With　the　continuous　emergence　of　new　knowledge,　Knowledge　Graph　(KG)　typically　suffers　from　the　incompleteness　problem,　hindering　the　performance　of　downstream　applications.　Thus,　Knowledge　Graph　Completion　(KGC)　has　attracted　considerable　attention.　However,　existing　KGC　methods　usually　capture　the　coarse-grained　information　by　directly　interacting　with　the　entity　and　relation,　ignoring　the　important　fine-grained　information　in　them.　To　capture　the　fine-grained　information,　in　this　paper,　we　divide　each　entity/relation　into　several　segments　and　propose　a　novel　Multi-Level　Interaction　(MLI)　based　KGC　method,　which　simultaneously　interacts　with　the　entity　and　relation　at　the　fine-grained　level　and　the　coarse-grained　level.　The　fine-grained　interaction　module　applies　the　Gate　Recurrent　Unit　(GRU)　mechanism　to　guarantee　the　sequentiality　between　segments,　which　facilitates　the　fine-grained　feature　interaction　and　does　not　obviously　sacrifice　the　model　complexity.　Moreover,　the　coarse-grained　interaction　module　designs　a　High-order　Factorized　Bilinear　(HFB)　operation　to　facilitate　the　coarse-grained　interaction　between　the　entity　and　relation　by　applying　the　tensor　factorization　based　multi-head　mechanism,　which　still　effectively　reduces　its　parameter　scale.　Experimental　results　show　that　the　proposed　method　achieves　state-of-the-art　performances　on　the　link　prediction　task　over　five　well-established　knowledge　graph　completion　benchmarks.