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In this paper, we propose a memory-efficient pipeline architecture which performs the one-level two-dimensional discrete wavelet transform (2D DWT) of the 9/7 filter for JPEG 2000. In general, the internal memory size of 2D architecture highly depends on the pipeline registers of 1D DWT. Based on the lifting-based DWT algorithm, the primitive data path is modified. Thus, an efficient pipeline architecture is derived to shorten the data path and decrease the internal memory size for 2D DWT. That is, for an N×M image, only 5.5N size memory is required for the 9/7 filter to perform the one-level 2D DWT decomposition with one multiplier delay (i.e. N and M indicate the height and width of an image). Based on the proposed architecture, the tradeoff between high speed and low internal memory for 2D DWT can be eased.