We　investigate　the　estimators　of　parameters　of　interest　for　a　single-index　varying-coefficient　model.　To　estimate　the　unknown　parameter　efficiently,　we　first　estimate　the　nonparametric　component　using　local　linear　smoothing,　then　construct　an　estimator　of　parametric　component　by　using　estimating　equations.　Our　estimator　for　the　parametric　component　is　asymptotically　efficient,　and　the　estimator　of　nonparametric　component　has　asymptotic　normality　and　optimal　uniform　convergence　rate.　Our　results　provide　ways　to　construct　confidence　regions　for　the　involved　unknown　parameters.　The　finite-sample　behavior　of　the　new　estimators　is　evaluated　through　simulation　studies,　and　applications　to　two　real　data　are　illustrated.