Parallel Halley iteration method, based on circular arithmetic for finding all zeros of a polynomial, avoids troublesome circular extraction operation,and the approximation with error estimation of all zeros of a polynomial can be obtained at the same time with it, and it has higher convergence rate , while it was synchronous parallel algorithm. The asynchronous parallel algorithm was constructed with circular arithmetic in order to find all zeros of a polynomial, and the convergence theory was established under the similar condition of Halley iteration method. The algorithm not only retain the advantage of Halley iteration method, but has better parallelism.