The notion of identity-based online/offline encryption (IBOOE) was recently introduced by Guo, Mu and Chen in FC 2008. In an IBOOE system, the encryption is split into online and offline phases. The offline phase is performed prior to the arrival of a message and the recipient's public key (or,identity). The online phase is performed very efficiently after knowing the message and public key. The IBOOE scheme is particularly useful for devices that have very low computation power since partof computation is conducted while the device is not busy. In this paper, we extend the notion of IBOOE to the hierarchical identity-based online/offline encryption (HIBOOE), and propose a "selective-ID" secure HIBOOE scheme from Boneh, Boyen and Goh's HIBE, where the online phase in HIBOOE is very efficient.