Encryption is an important technique to improve information security for many real-world applications. The Advanced Encryption Standard (AES) is a widely-used efficient cryptographic algorithm. Although AES is fast both in software and hardware, it is time-consuming to do data encryption especially for large amount of data. Therefore, it is a lasting effort to accelerate AES operations. This paper presents SW-AES, a parallel AES implementation on the Sunway TaihuLight, one of the fastest supercomputers in the world that takes the SW26010 processor as the basic building block. According to the architectural features of SW26010, SW-AES exploits parallelism from different levels, including (1) inter-CPE (Computing Processing Element) data parallelism that distributes tasks among the 256 on-chip CPEs, (2) intra-CPE data parallelism enabled by the Single-Instruction Multiple-Data (SIMD) instructions inside each CPE, and (3) instruction-level parallelism that pipelines memory access and the computation. In addition, corresponding to the two application scenarios, SW-AES presents scalable ways to efficiently run AES on many nodes. As a result, SW-AES can gain a maximum throughput of 13.50 GB/s on a single SW26010 node, which is 216.23x higher than the latest parallel AES implementation on the Sunway TaihuLight, and about 37.3% higher than the latest AES implementation on the GTX 480 GPU. When running on 1024 computing nodes with each one processing 1 GB data, SW-AES can achieve a throughput of 13819.25 GB/s. On the contrast, only a throughput of 63.91 GB/s can be achieved by the latest related work on the Sunway TaihuLight.