Due to the increasing capabilities of cybercriminals and the vast quantity of sensitive data, it is necessary to protect remote sensing images during data transmission with “Belt and Road” countries. Joint image compression and encryption techniques exhibit reliability and cost-effectiveness for data transmission. However, the existing methods for multiband remote sensing images have limitations, such as extensive preprocessing times, incompatibility with multiple bands, and insufficient security. To address the aforementioned issues, we propose a joint encryption and compression algorithm (JECA) for multiband remote sensing images, including a preprocessing encryption stage, crypto-compression stage, and decoding stage. In the first stage, multiple bands from an input image can be spliced together in order from left to right to generate a grayscale image, which is then scrambled at the block level by a chaotic system. In the second stage, we encrypt the DC coefficient and AC coefficient. In the final stage, we first decrypt the DC coefficient and AC coefficient, and then restore the out-of-order block through the chaotic system to get the correct grayscale image. Finally, we postprocess the grayscale image and reconstruct it into a remote sensing image. The experimental results show that JECA can reduce the preprocessing time of the sender by 50% compared to existing joint encryption and compression methods. It is also compatible with multiband remote sensing images. Furthermore, JECA improves security while maintaining the same compression ratio as existing methods, especially in terms of visual security and key sensitivity.