Nowadays, steganalysis of JPEG images is increasingly popular because of their widespread usage. The DCTR set (Discrete Cosine Transform Residual) is a significant steganalysis feature set designed for the JPEG images. Its main advantage is its low computational complexity, while providing high accuracy in detection. However, it is desirable to further accelerate it, especially for some real-time applications. In this paper, we accelerate the DCTR features extraction on a GPU device, and some optimization methods are presented. Firstly, we utilize the separability and symmetry of the two-dimensional discrete cosine transform to enhance the computing efficiency in decompression and filtering images. Secondly, when computing phase-aware histograms, in order to achieve a good coalesced access and avoid the serious collisions between atomic operations, we add different off-sets to the elements of the residual according to their positions, which implies the computation of phase-aware histograms can be converted into the computation of ordinary 256-dimensional histograms. By this means, we can fully exploit the GPU's parallelism. The experimental results show that the speed of our parallel method for images with different sizes is 150-200 times faster than the original serial method on our machine. Our method can also be applied to other phase-aware feature sets, such as PHARM (PHase Aware pRojection Mode).