We　study　the　stability　of　the　critical　defocusing　semilinear　wave　equation　with　a　distributed　locally　damping　and　Dirichlet-Neumann　boundary　condition　on　a　bounded　domain.　The　main　novelty　is　to　establish　a　framework　to　study　the　stability　of　the　damped　critical　semilinear　wave　equation　on　bounded　domain.　The　unique　continuation　properties　and　the　observability　inequalities　are　proved　by　the　Morawetz　estimates　in　Euclidean　spaces,　and　then　the　compactness-uniqueness　arguments　are　applied　to　prove　the　main　stabilization　result.　(c)　2021　Elsevier　Inc.　All　rights　reserved.