We　study　the　boundary　stabilization　of　a　semilinear　wave　equation　with　variable　coefficients　under　the　time-varying　and　nonlinear　feedback.　By　the　Riemannian　geometry　methods,　we　obtain　the　stability　results　of　the　system　under　suitable　assumptions　of　the　bound　of　the　time-varying　term　and　the　nonlinearity　of　the　nonlinear　term.