In　this　paper,　we　consider　the　estimation　problem　of　quantile　varying-coefficient　models　when　the　link　function　is　unspecified,　which　significantly　expands　the　existing　works　on　varying-coefficient　models　with　unspecified　link　function　focusing　only　on　mean　regression.　We　provide　new　identification　conditions　which　are　weaker　than　existing　ones.　Under　these　identification　conditions,　we　use　polynomial　splines　to　estimate　both　the　varying　coefficients　and　the　link　functions　and　establish　the　convergence　rate　of　the　estimator.　Our　simulation　studies　and　a　real　data　application　illustrate　the　finite　sample　performance　of　the　estimators.