The measurement of visual quality is of fundamental importance to remote sensing image compression, especially for image quality assessment and compression algorithm optimization. We exploit the distortion features of optical remote sensing image compression and propose a full-reference image quality metric based on multilevel distortions (MLD), which assesses image quality by calculating distortions of three levels (such as pixel-level, contexture-level, and content-level) between original images and compressed images. Based on this, a multiscale MLD (MMLD) algorithm is designed and it outperforms the other current methods in our testing. In order to validate the performance of our algorithm, a special remote sensing image compression distortion (RICD) database is constructed, involving 250 remote sensing images compressed with different algorithms and various distortions. Experimental results on RICD and Laboratory for Image and Video Engineering databases show that the proposed MMLD algorithm has better consistency with subjective perception values than current state-of-the-art methods in remote sensing image compression assessment, and the objective assessment results can show the distortion features and visual quality of compressed image well. It is suitable to be the evaluation criteria for optical remote sensing image compression.