Dictionary-based encoding methods are popular forms of data compression. These methods were initially implemented to reduce the one-dimensional correlation in data, since they are designed to compress text. Therefore, they do not take advantage of the fact that adjacent pixels in images are correlated in two dimensions. Previous attempts have been made to adapt dictionary-based compression schemes to consider the two-dimensional nature of images, but mostly for binary images. In this paper, a two-dimensional dictionary-based lossless image compression scheme for grayscale images is introduced. The proposed scheme reduces correlation in image data by finding two-dimensional blocks of pixels that are approximately matched throughout the data and replacing them with short codewords. Test results show that the compression performance of the proposed scheme outperforms and surpasses any other existing dictionary-based lossless compression scheme. The results also show that it slightly outperforms JPEG-2000s compression performance, when it operates in its lossless mode, and it is comparable to JPEG-LS's and CALIC's compression performance, where JPEG-2000 and JPEG-LS are the current image compression standards, and CALIC is a Context-based Adaptive Lossless Image Coding scheme.