The major drawback of the fractal image compression is the high encoding complexity to find the best match between a range block and a large pool of domain blocks. This paper presents a fast fractal-encoding algorithm based on the law of cosines. The number of domain blocks searched to find the best match for each range block is safely reduced by eliminating the ineligible domain blocks using the law of cosines. Simulation results show that the proposed algorithm can produce a completely identical fractal code to that of the exhaustive search in reduced time.