Identity-based cryptography is proposed to solve the complicated certificate management of traditional public-key cryptography. The pairing computation and high-level tower extension field arithmetic turn out to be the performance bottleneck of pairing-based signature schemes. Graphics processing units have been increasingly popular for general-purpose computing in recent years. They have shown a lot of promise in speeding up cryptographic schemes such as AES, RSA, and ECDSA. However, to our knowledge, the research on parallel implementation of pairings and identity-based cryptographic schemes on graphics processing units is somewhat outdated. Therefore, in this article, we implement the identity-based signature scheme in the IEEE P1363 Standard on a modern NVIDIA RTX 3060 card. We convert the pairing computation in signature verification into a product of pairings with fixed arguments and therefore avoid the scalar multiplication in 𝔾 2 . Then we employ the precomputation technique to improve the elliptic curve scalar multiplication, exponentiation in \(\mathbb {F}_{p^{12}}\) and the pairing computation. We also apply PTX ISA to multiple-precision arithmetic. Experiments demonstrate that our implementation can perform 43,856/46,753/39,798 pairings/sec for the Optimal Ate pairing, the pairing with a fixed argument, and two pairings with fixed arguments, respectively. Peak throughputs of signature generation and verification can achieve 322.6 and 40.6 kops/sec over the BN254 curve.