In this letter, we propose a shape-adaptive (SA) reversible integer lapped transform (SA-RLT) method. The new method can deal with arbitrarily shaped image areas while guaranteeing completely reversible integer-to-integer transform. Based on SA-RLT and object-based set partitioned embedded block coder, a new region-of-interest (ROI) compression scheme is designed for 2-D remote sensing images. Numerical experiments reveal that SA-RLT performs better than integer SA discrete wavelet transform, and the new ROI compression scheme performs comparably even better than the JPEG2000-ROI scheme. Advantages in hardware implementation have been preserved by SA-RLT, such as parallel processing and low memory requirement.