The explosive growth of images and videos on the World Wide Web (WWW) is making the Web into a huge resource of visual information. Among various types of multimedia information, still images or dynamic images (video clips) in compressed format are the most widely accepted on the WWW. Therefore, it becomes an essential issue to achieve the maximum efficiency in transmitting and decoding those compressed images on the Internet. Progressive coding provides a mode that allows a coarse version of an image being transmitted at a lower bit rate and then gradually refined by subsequent transmissions. Compared with conventional coding, it is more suitable for interactive applications such as those involving JPEG images on the Internet. In this paper, we first give an approximation of cosine function used in IDCT for the various orders. Based on the approximation and a series analysis, we then develop a progressive decoding scheme which comprehends the successive approximation and the spectral selection. The analysis and experiments establish the fact that our proposed method saves computational cost significantly in comparison with the existing spectral selection based progressive decoding proposed by JPEG. Extensive experiments are carried out to evaluate the proposed algorithm, which reveals that, the reconstructed images, even at the lowest bit rate and with lower order approximation, can still achieve encouraging PSNR values.