A new processing algorithm based on fractal image compression is proposed for image processing efficiency. An image will partition into non-overlapping blocks called range blocks and overlapping blocks called domain blocks, with the domain blocks generally bigger than the range blocks, to achieve a rapid encoding time. This research introduced a new fast full-search algorithm approach that starts the search for the best matching domain in the range block from the closest points in the range blocks and expands the search until an acceptable match is found or the search is completed to save even more encoding time. The proposed fast full-search approach, despite its simplicity, is more efficient than the standard search method. The search reduction, peak signal to noise ratio, compression ratio, and encoding time of the suggested approach are all examined. The proposed method can encode a 512x512 grayscale Lena image in 0.36 seconds, with a total search reduction of 87% according to experimental results.