The rapidly growing location-based services enable service providers to accumulate plentiful descriptions on points of interest (POIs), which can be used to support expressive POI queries. In this article, we study a type of POI query, named feature-based group <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> nearest neighbor query over road networks, in which a user has a feature set and several locations and wishes to find <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> closest POIs that have similar sets of features to the query. As the POI data sets grow, service providers tend to outsource their data sets to a powerful yet not-fully trusted cloud, which calls for privacy preservation on data sets and user queries. Although many schemes have been proposed for privacy-preserving POI queries, none of them can simultaneously support privacy-preserving set similarity and road network distance comparison. To address this challenge, we propose an efficient and private feature-based group nearest neighbor query scheme. In our scheme, we achieve privacy-preserving distance comparison by employing the road network hypercube embedding technique, and design an encrypted index based on B+-tree for privacy-preserving set similarity range queries. Security analysis shows our proposed scheme can preserve the privacy of the data set and queries, and performance evaluation also demonstrates it is computationally efficient.