An adaptive regularity scalable wavelet image coding algorithm is proposed in this paper. The bitstream is generated in the order of regularity such that visually more important components of a decoded image can be obtained first, followed by the higher regularity components as more bits are received and decoded. The scalability is achieved by selecting different extents of wavelet coefficients at various regularity levels. These regularity levels are determined adaptively. Regularity of the image is estimated from the interscale ratios of the separable wavelet transform magnitude sums. Compared to the wavelet image coder generating resolution scalable bitstreams, significant improvement in visual quality and PSNR can be achieved.