Genomic data is being produced rapidly by both individuals and enterprises, and outsourcing this ever-increasing data into clouds is promising for cutting the cost of data owners and mining the wealth of genomic data at a larger scale. However, genome carries sensitive information about individuals, and it is challenging to securely and efficiently perform analysis on remotely hosted genomic databases. In this paper, we present a privacy-preserving range-constrained intersection query scheme on genomic data. To achieve security and efficiency, we propose a protocol to fulfill range-constrained intersection query, named PriRanGe. With PriRanGe, a client can securely query genomic data in a specific range in a database while keeping this whole process private. The security of our design targets genomic database confidentiality, query range/result confidentiality, and access pattern protection, and the advantage in efficiency is due to most employed primitives are symmetric. We thoroughly evaluated our design by security proof, experimental analysis and comparison to the state-of-the-art works, all of which support the conclusion that this design is both secure and fast.