Galindo-Garcia identity-based signature (GG09 IBS) is an efficient identity-based signature (IBS) based on Schnorr signature scheme. The security of GG09 IBS is proven in the random oracle model under the discrete-log assumption, however, the security proof achieves a loose security only. In CANDAR'17, Fukumitsu and Hasegawa proposed a GG09-like IBS (FH17 IBS). Although their scheme achieves a tight security in the random oracle model under the DDH assumption, the size of components and the computational time is much worse than the original GG09 IBS. In this paper, we revisit FH17 IBS and propose an IBS which is more efficient than FH17 IBS. Our proposed IBS has a tight security in the random oracle model under the DDH assumption as well as FH17 IBS and has about 2 times efficiency than FH17 scheme. The security proof of our scheme utilizes the property of our scheme that the user key generation algorithm is probabilistic.