Discrete cosine transform (DCT) based JPEG standard significantly improves the coding efficiency of image compression, but it is unacceptable event in serious blocking artifacts at low bit rate and low efficiency of high-definition image. In the light of all phase digital filtering theory, this paper proposes a novel transform based on discrete sine transform (DST), which is called all phase discrete sine biorthogonal transform (APDSBT). Applying APDSBT to JPEG scheme, the blocking artifacts are reduced significantly. The reconstructed image of APDSBT-JPEG is better than that of DCT-JPEG in terms of objective quality and subjective effect. For improving the efficiency of JPEG coding, the structure of JPEG is analyzed. We analyze key factors in design and evaluation of JPEG compression on the massive parallel graphics processing units (GPUs) using the compute unified device architecture (CUDA) programming model. Experimental results show that the maximum speedup ratio of parallel algorithm of APDSBT-JPEG can reach more than 100 times with a very low version GPU. Some new parallel strategies are illustrated in this paper for improving the performance of parallel algorithm. With the optimal strategy, the efficiency can be improved over 10%.