Target tracking algorithms for moving targets in acoustic vector-sensor array are investigated and an efficient Direction Of Arrival(DOA) tracking algorithm for acoustic vector-sensor array based on Projection Approximation and Subspace Tracking of deflation(PASTd) is proposed. The proposed algorithm uses PASTd method to track the DOA of received signals for acoustic vector-sensor arbitrary array, and owing to the fast convergence features, it holds the properties of lower computational complexity. Furthermore, the proposed algorithm outperforms the PAST method in terms of angle tracking accuracy. A series of simulation results verify the effectiveness of the algorithm.