The inherent random-like behavior and one-way property of iteration in chaotic systems provide a good basis for designing Hash function. In the era of big data, due to the increasing data capacity in applications, fast Hash functions with parallel mode are highly desirable when authenticating data integrity. We analyze the issue of how to parallelize Hash function with iterative structure. Some security requirements on parallel Hash function are presented. In addition, using chaotic map and block cipher, we construct a keyed parallel Hash function. The message blocks are firstly processed in parallel by a DM-like structure. Furthermore, a tree mode with chaotic map is utilized to combine the outputs of the hash round function in parallel. The proposed Hash function is analyzed by theory and tested by computer simulations. The test results show that the proposed scheme can resist the various common attacks against Hash functions. It satisfies the secure performance requirements of Hash function. Owing to the usage of the parallel mode to process messages, the proposed chaos-based Hash function possess high efficiency and has high potential in applications to guarantee data integrity on a parallel computing platform.