Abstract: Aiming at the problem of near-field sound source localization estimation under the condition of less array elements than sources, the method of sparse reconstruction based on Khatri-Rao (KR) product is proposed. The source signals are wide-sense quasi-stationary in this method. A virtual array structure is acquired by KR product and the degree of freedom is increased. In the virtual array structure the spectra of the sound sources are acquired band on sparse reconstruction, which is solved by l₁ norm method. Simulations demonstrate the proposed method can realized underdeterminded estimation of sound source and the performance is better than the subspace method.