We　consider　the　problem　of　variable　selection　for　single-index　varying-coefficient　model,　and　present　a　regularized　variable　selection　procedure　by　combining　basis　function　approximations　with　SCAD　penalty.　The　proposed　procedure　simultaneously　selects　significant　covariates　with　functional　coefficients　and　local　significant　variables　with　parametric　coefficients.　With　appropriate　selection　of　the　tuning　parameters,　the　consistency　of　the　variable　selection　procedure　and　the　oracle　property　of　the　estimators　are　established.　The　proposed　method　can　naturally　be　applied　to　deal　with　pure　single-index　model　and　varying-coefficient　model.　Finite　sample　performances　of　the　proposed　method　are　illustrated　by　a　simulation　study　and　the　real　data　analysis.