This paper presents a study on a high-performance design for a block cipher algorithm implemented on modern many-core graphics processing units (GPUs). The recent emergence of VLSI technology makes it feasible to fabricate multiple processing cores on a single chip and enables general-purpose computation on a GPU (GPGPU). The GPU strategy offers significant performance improvements for all-purpose computation and can be used to support a broad variety of applications, including cryptography. We have proposed an efficient implementation of the encryption/decryption operations of a block cipher algorithm, SEED, on off-the-shelf NVIDIA many-core graphics processors. In a thorough experiment, we achieved high performance that is capable of supporting a high network speed of up to 9.5 Gbps on an NVIDIA GTX285 system (which has 240 processing cores). Our implementation provides up to 4.75 times higher performance in terms of encoding and decoding throughput as compared to the Intel 8-core system.