Evolutionary optimized coefficients of discrete orthogonal Tchebichef moment transform (TMT) are utilized in this study to ameliorate the quality of the traditional moments-based image compression methods. Most of the existing methods compute moment-transform coefficients for the input image and then select the coefficients sequentially downward to a certain order based on the desired compression ratio. However, the proposed method divides the input image into nonoverlapping square blocks of specific size in order to circumvent the problem of numerical instability and then computes the TMT coefficients for each block. In this work, a real-coded genetic algorithm is employed to optimize the TMT coefficients of each block, which produces reconstructed images of better quality for the desired compression ratio. Here the optimization is carried out by minimizing the mean square error function. Standard test images of two different sizes (128 × 128 and 256 × 256) have been subjected to the proposed compression method for the block sizes (4 × 4 and 8 × 8) in order to assess its performance. The results reveal that the proposed real-coded genetic algorithm-based method outperforms others, namely the conventional sequential selection method and simple random optimization method, for the chosen input images in terms of the task of compression.