The main challenge at present in constructing hierarchical identity-based encryption (HIBE) is to solve the trade-off between private-key size and ciphertext size. At least one private-key size or ciphertext size in the existing schemes must rely on the hierarchy depth. In this letter, a new hierarchical computing technique is introduced to HIBE. Unlike others, the proposed scheme, which consists of only two group elements, achieves constant-size private keys. In addition, the ciphertext consists of just three group elements, regardless of the hierarchy depth. To the best of our knowledge, it is the first efficient scheme where both ciphertexts and private keys achieve O(1)-size, which is the best trade-off between private-key size and ciphertext size at present. We also give the security proof in the selective-identity model.