The purpose of this paper is to address the performance degradation when using acoustic vector sensor array (AVSA) in impulsive noise environment for estimating direction of arrival (DOA). The existing methods of DOA estimation generally assume that the noise in the signal is Gaussian white noise. However, owing to the complexity of the underwater environment, the noise may contain impulsive characteristics, which will invalidate the original DOA estimation methods. In order to realize stable DOA estimation using AVSA in impulsive noise, a novel algorithm for sparse iteration based on bounded nonlinear function (BNF) and low-order processing is proposed in this paper. Firstly, the BNF is applied to suppress outliers caused by impulsive noise. Then, to overcome the limitation of BNF, which can only suppress impulsive noise in the nonlinear region, a sparse iterative technique based on low-order processing is applied. Finally, the DOA estimation is obtained through spectral peak search. The results of simulation indicate that the proposed algorithm can provide superior suppression of impulsive noise and significantly improves the performance of DOA estimation compared to existing methods. And this superiority is further outstanding when the generalized signal-to-noise ratio (GSNR) and the snapshots are small.