Image enhancement plays a very crucial role in many image processing applications. It aims at improving the visual and informational quality of the distorted images. Histogram equalization is one of the most frequently used techniques for image contrast enhancement. However, histogram and most of the other enhancement approaches may yield un-natural looking or artifacts after enhancement, and the images computed by these methods are not desirable in few applications such as consumer electronic products where brightness preservation is necessary to avoid annoying artifacts. To overcome such problems, a new optimal grey level mapping based edge preserved satellite images enhancement technique using a beta differential evolution (BDE) algorithm has been proposed in this paper. The proposed method uses a simple grey-level mapping technique and beta differential evolution algorithm together with corresponding enhancement operators for quality contrast and brightness boosting of the satellite images. In this approach, the grey levels of the input image are replaced by a new set of grey levels. The proposed algorithm has been tested on numerous colored satellite images and also on standard Lena image. Further qualitative and statistical comparisons of the proposed BDE with artificial bee colony, modified artificial bee colony, particle swarm optimization, differential evolution algorithms are presented in the paper, which have proven its superiority in terms of PSNR, MSE, SSIM, FSIM and EKI indices.