Abstract: Based on the sparse representation of the array covariance matrix and the Khatri-Rao product of the array response matrix, a low computational complexity sparse recovery method for direction-of-arrival (DOA) estimation is presented. The proposed algorithm not only lessens the number of unknown variable, but also can cut down the dimension of the constraints, which considerably reduce the computational complexity of the second order cone programming. Moreover, a weighted l₁ minimization is designed by using the reciprocal of the Capon spectrum as a weighting vector. As a result, the proposed algorithm can achieve better performance while the computational complexity is reduced. Simulations demonstrate the performance of the proposed method.