We　study　the　stabilization　of　the　wave　equation　with　variable　coefficients　in　a　bounded　domain　and　a　time-varying　and　nonlinear　term.　By　the　Riemannian　geometry　methods　and　a　suitable　assumption　of　nonlinearity　and　the　time-varying　term,　we　obtain　the　uniform　decay　of　the　energy　of　the　system.