In this paper, we analyze collision resistance of the JH hash function in the ideal primitive model. The JH hash function is one of the five SHA-3 candidates accepted for the final round of evaluation. The JH hash function uses a mode of operation based on a permutation, while its security has been elusive even in the random permutation model. One can find a collision for the JH compression function only with two backward queries to the basing primitive. However, the security is significantly enhanced in iteration. For c≤ n/2, we prove that the JH hash function using an ideal -bit permutation and producing -bit outputs by truncation is collision resistant up to O(2c/2)queries. This bound implies the optimal collision resistance of the JH hash function in the random permutation model.