This paper combines the parameters estimation problem of acoustic vector-sensor array with the parallel factor （PARAFAC） model， and proposes a fast PARAFAC decomposition-based two-dimensional direction of arrival （DOA） estimation algorithm. The proposed algorithm first constructs the received data as PARAFAC model， then the parameter matrices are initially estimated in data field and the two-dimensional DOA estimation can be obtained via fast PARAFAC decomposition. The proposed algorithm is effective for arbitrary acoustic vector-sensor array and can acquire automatically paired angle estimations. Furthermore， owing to the initial estimation of the PARAFAC model， the proposed algorithm owns the faster PARAFAC decomposition and the lower computational complexity. The simulation results indicate that the angle estimation performance of the proposed algorithm is close to that of the traditional PARAFAC algorithm and better than that of the estimation of signal parameters via rotational invariance techniques （ESPRIT） and the propagator method （PM）.