Subband/DCT coding has been introduced in order to transmit images of various resultions using one given image-codec, for nowadays there are various grades of quality in visual communication services. However, subband/DCT results in the increawse of multiplication number and memory size. In order to resolve this problem, we propose block-based subband/DCT coding in this paper. In block-based subband/DCT, the number of multiplications is not only reduced because we combine subband decomposistion with DCT, but the size of memory is also reduced because images can be parallel-processed block by block. We show that the number of multiplications is reduced, by analyzing the property ofblock-based subband/DCT matrix mathematically, and examine the performance of proposed coder, which adopts JPEG as backhand-coder after block-based subband/DCT.