Image compression is considered to be one of the most important problems in computer storage and transmission. Various compression methods have been introduced to achieve high compression ratios and high image qualities in low computational time. Fractal Image Compression is one of the techniques that offers an advantage in reconstructing images of high quality with reasonable compression ratio and fast decoding process. But, on the other hand, the encoding part of this method is considered to be highly time-consuming process. The time consumption is a result of the matching block process used for eight orients. This study proposes a method with new approach of matching with one computed affine transformation to accelerate the encoding time, which increases the efficiency to approximately ten times the traditional method for the same image size and block number. The difference between the encoding time for the two methods is proportional to number of blocks, which leads to high performance. The rate of encoding time with block number is very small compared to the traditional method, which leads to increase in its competitively compared with all other methods. However, the proposed method still produces a comparable reconstructed image quality and compression ratio comparable to that seen in Traditional Fractal Image Compression.