The Internet of Things (IoT) boom has enabled Internet Service Providers (ISPs) to collect an enormous amount of high-dimensional data. Performing range queries on such data can effectively reuse them to help ISPs offer better services. Owing to the low cost and high resource utilization of cloud computing, an increasing number of ISPs are inclined to outsource data and services to it. However, as the cloud is not fully trusted, data need to be encrypted before being outsourced, which inevitably hinders many query services, e.g., range queries. Various schemes were proposed for privacy-preserving range queries, yet they struggled to extend to high-dimensional scenarios and did not support dimension selection. Aiming at this challenge, in this paper, we propose an efficient and privacy-preserving high-dimensional range query scheme (PHRQ) based on an iMinMax tree while supporting dimension selection. Specifically, we first build an iMinMax tree for high-dimensional data and utilize a symmetric homomorphic encryption technique to design a suite of privacy-preserving protocols to achieve secure high-dimensional range queries. Then, we design a sub-dimensional range determination protocol to support dimension selection. Further, based on the iMinMax tree and our privacy-preserving protocols, we propose our PHRQ scheme. Finally, security analysis shows that our scheme is privacy-preserving, and performance evaluation demonstrates that our scheme is efficient in high-dimensional range query processing.