RC6 was a candidate encryption algorithm for AES selections which emphasizes on the security, simplicity and performance of the algorithm. The round keys of RC6 are generated from the input key words by a certain amount of “one-way” according to the authors’ claims. For the above two reasons, in this paper, we describe a hash func-tion, named the RC hash function based on the use of the underlying RC6 encryption algorithm. It is thus natural that the strength of our proposed scheme relies to a large extent on the RC6 encryption algorithm. The RC hash function in our study can generate 128-bit output. Furthermore, we also give variants of the RC hash function that can output 192 and 256 bits, respectively.