In　this　paper,　we　show　that　the　quadratic　assignment　problem　(QAP)　can　be　reformulated　to　an　equivalent　rank　constrained　doubly　nonnegative　(DNN)　problem.　Under　the　framework　of　the　difference　of　convex　functions　(DC)　approach,　a　semi-proximal　DC　algorithm　is　proposed　for　solving　the　relaxation　of　the　rank　constrained　DNN　problem　whose　subproblems　can　be　solved　by　the　semi-proximal　augmented　Lagrangian　method.　We　show　that　the　generated　sequence　converges　to　a　stationary　point　of　the　corresponding　DC　problem,　which　is　feasible　to　the　rank　constrained　DNN　problem　under　some　suitable　assumptions.　Moreover,　numerical　experiments　demonstrate　that　for　most　QAP　instances,　the　proposed　approach　can　find　the　global　optimal　solutions　efficiently,　and　for　others,　the　proposed　algorithm　is　able　to　provide　good　feasible　solutions　in　a　reasonable　time.