ID-based authenticated key exchange (ID-AKE) is a cryptographic tool to establish a common session key between parties with authentication based on their IDs. If IDs contain some hierarchical structure such as an e-mail address, hierarchical ID-AKE (HID-AKE) is especially suitable because of scalability. However, most of existing HID-AKE schemes do not satisfy advanced security properties such as forward secrecy, and the only known strongly secure HID-AKE scheme is inefficient. In this paper, we propose a new HID-AKE scheme which achieves both strong security and efficiency. We prove that our scheme is eCK-secure (which ensures maximal-exposure-resilience including forward secrecy) without random oracles, while existing schemes is proved in the random oracle model. Moreover, the number of messages and pairing operations are independent of the hierarchy depth; that is, really scalable and practical for a large-system.