This paper provides a sufficient condition to construct timed-release public-key encryption (TRPKE), where the constructed TRPKE scheme guarantees strong security against malicious time servers, proposed by Chow et al., and strong security against malicious receivers, defined by Cathalo et al., in the random oracle model if the component IBE scheme is IND-ID-CPA secure, the component PKE scheme is IND-ID-CPA secure, and the PKE scheme satisfies negligible γ-uniformity for every public key. Although Chow et al. proposed a strongly secure TRPKE scheme, which is concrete in the standard model, to the best of our knowledge, the proposed construction is the first generic one for TRPKE that guarantees strong security even in the random oracle model.