We propose an algorithm for fast computation of three-dimensional (3-D) Hahn moments. First, the symmetry property of Hahn polynomials is provided to decrease the computational complexity at 12%. Second, 3-D Hahn moments are computed by using an algorithm based on matrix multiplication. The proposed algorithm enormously reduces the computational complexity of a 3-D Hahn moment and its inverse moment transform. It can be also implemented easily for high order of moments. The performance of the proposed algorithm is proved through object reconstruction experiments. The experimental results and complexity analysis show that the proposed method outperforms the straightforward method, especially for large size noise-free and noisy 3-D objects.