The longest common subsequence (LCS) for two given strings has various applications, such as for the comparison of deoxyribonucleic acid (DNA). In this paper, we propose a graphics processing unit (GPU) algorithm to accelerate Hirschberg's LCS algorithm improved with Crochemore et al.'s bit-parallel algorithm. Crochemore et al.'s algorithm includes bitwise logical operators, which can be computed easily in parallel because they have bitwise parallelism. However, Crochemore et al.'s algorithm also includes an operator with less parallelism, i.e., an arithmetic sum. In this paper, we focus on how to implement these operators efficiently in parallel and experimentally show the following results. First, the proposed GPU algorithm with a 2.67GHz Intel Core i7 920 CPU and GeForce GTX 580 GPU performs a maximum of 12.81 times faster than the bit-parallel CPU algorithm using a single-core 2.67GHz Intel Xeon X5550 CPU. Subsequently, the proposed GPU algorithm executes a maximum of 4.56 times faster than the bit-parallel CPU algorithm using a four-core 2.67GHz Intel Xeon X5550 CPU. Furthermore, the proposed algorithm with GeForce 8800 GTX performs 10.9 to 18.1 times faster than Kloetzli et al.'s existing GPU algorithm with the same GPU.