We discuss the impossible differential cryptanalysis of the block cipher Zodiac . The main design principles of Zodiac are simplicity and efficiency. However the diffusion layer in its round function is too simple to offer enough security. An impossible differential cryptanalysis is a proper method to attack the weakness of Zodiac. Our attack using two 14-round impossible characteristics derives 128-bit master key of the full 16-round Zodiac with its complexity 2119 encryption times faster than the exhaustive search. The efficiency of the attack compared with exhaustive search increases as the key size increases.