This paper presents an Adaptive Multi-directional Max-plus algebra-based Morphological wavelet Transform (AM-MMT). The AM-MMT is based on a conventional max-plus algebra-based morphological wavelet transform and utilizes several suitable sampling windows that are adaptively selected in accordance with the direction of the content in the image. Thus, this proposed method extracts directional structures smoothly to calculate nonlinear operation (maximum or minimum search) and the standard sum. To show the effectiveness of the AM-MMT, nine standard benchmark images were used to compare the AM-MMT with the conventional MMT. From the experiment, transformed-images can be made by combining the high quality parts of the images, which are processed by each sampling window. All the PSNR values of the AM-MMT are higher than those of the conventional MMT with increasing deletion bit width. Thus, the AM-MMT achieves high-quality high-compression digital images. Furthermore, the expansion into the multi-level AM-MMT operation is described, and a Level 2 (L2) implementation example is shown. The L2 AM-MMT compressed-image is up to about 82% smaller than the original image. Consequently, the AM-MMT can accomplish effective nonlinear operation-based image transformation.