We　prove　the　exponential　stability　of　the　defocusing　critical　semilinear　wave　equation　with　variable　coefficients　and　locally　distributed　damping　on　R-3.　The　construction　of　the　variable　coefficients　is　almost　equivalent　to　the　geometric　control　condition.　We　develop　the　traditional　Morawetz　estimates　and　the　compactness-uniqueness　arguments　for　the　semilinear　wave　equation　to　prove　the　unique　continuation　result.　The　observability　inequality　and　the　exponential　stability　are　obtained　subsequently.