In hyperspectral imagery, greedy modular eigenspace (GME) was developed by clustering highly correlated bands into a smaller subset based on the greedy algorithm. Unfortunately, GME is hard to find the optimal set by greedy scheme except by exhaustive iteration. The long execution time has been the major drawback in practice. Accordingly, finding the optimal (or near-optimal) solution is very expensive. Instead of adopting the band-subset-selection paradigm underlying this approach, we introduce a simulated annealing band selection (SABS) approach, which takes sets of non-correlated bands for high-dimensional remote sensing images based on a heuristic optimization algorithm, to overcome this disadvantage. It utilizes the inherent separability of different classes embedded in high-dimensional data sets to reduce dimensionality and formulate the optimal or near-optimal GME feature. Our proposed SABS scheme has a number of merits. Unlike traditional principal component analysis, it avoids the bias problems that arise from transforming the information into linear combinations of bands. SABS can not only speed up the procedure to simultaneously select the most significant features according to the simulated annealing optimization scheme to find GME sets, but also further extend the convergence abilities in the solution space based on simulated annealing method to reach the global optimal or near-optimal solution and escape from local minima. The effectiveness of the proposed SABS is evaluated by NASA MODIS/ASTER (MASTER) airborne simulator data sets and airborne synthetic aperture radar images for land cover classification during the Pacrim II campaign. The performance of our proposed SABS is validated by supervised k-nearest neighbor classifier. The experimental results show that SABS is an effective technique of band subset selection and can be used as an alternative to the existing dimensionality reduction method.