Up to date, a large number of ID-based signature (IBS) schemes based on bilinear pairings have been proposed. Most of these IBS schemes possess existential unforgeability under adaptive chosen-message attacks, among which some offer strong unforgeability. An IBS scheme is said to be strongly unforgeable if it possesses existential unforgeability and an adversary who is given signatures of the IBS scheme on some message m is unable to generate a new signature on m. Strong unforgeable IBS schemes can be used to construct many important ID-based cryptographic schemes. However, the existing strongly unforgeable IBS schemes lack efficiency for the signature size and the computation cost of verification phase. In this paper, we propose an efficient strongly unforgeable IBS scheme without random oracles. Under the computational Diffie–Hellman and collision resistant hash assumptions, we demonstrate that the proposed IBS scheme possesses strong unforgeability against adaptive chosen-message attacks. When compared with previously proposed strongly unforgeable IBS schemes, our scheme has better performance in terms of signature size and computation cost.