Data outsourcing to cloud has been a common IT practice nowadays due to its significant benefits. Meanwhile, security and privacy concerns are critical obstacles to hinder the further adoption of cloud. Although data encryption can mitigate the problem, it reduces the functionality of query processing, e.g., disabling SQL queries. Several schemes have been proposed to enable one-dimensional query on encrypted data, but multi-dimensional range query has not been well addressed. In this paper, we propose a secure and scalable scheme that can support multi-dimensional range queries over encrypted data. The proposed scheme has three salient features: (1) Privacy: the server cannot learn the contents of queries and data records during query processing. (2) Efficiency: we utilize hierarchical cubes to encode multi-dimensional data records and construct a secure tree index on top of such encoding to achieve sublinear query time. (3) Verifiability: our scheme allows users to verify the correctness and completeness of the query results to address server's malicious behaviors. We perform formal security analysis and comprehensive experimental evaluations. The results on real datasets demonstrate that our scheme achieves practical performance while guaranteeing data privacy and result integrity.