Considering that the conventional beam forming based on an acoustic vector sensor array (AVSA) cannot demonstrate the anti-interference capability of AVSA, a direction estimation algorithm based on the signal subspace projection is put forward. In this paper, the 3rd order tensor of the received signals from AVSA is modeled and the signal subspace is derived from higher order singular value decomposition(HOSVD) and the calculation process of spatial spectrum is given by the projection of array manifold vector onto it ,exploiting multidimensional data structure inherently, with lower side lobe which can suppress noise sufficiently. The simulation result shows that the proposed algorithm is feasible which has important engineering significance.