In　this　article,　we　consider　the　problem　of　estimation　of　the　single-index　varying-coefficient　model　when　covariates　are　not　fully　observed.　By　using　the　bias-correction　and　inverse　selection　probability　methods,　a　weighted　estimating　equations　estimator　for　the　index　parameters　with　missing　covariates　is　constructed,　and　its　asymptotic　properties　has　been　established.　The　local　linear　estimator　for　the　coefficient　functions　is　proved　to　converge　at　an　optimal　rate.　Numerical　studies　based　on　simulation　and　application　suggest　that　the　proposed　estimation　procedure　is　powerful　and　easy　to　implement.