Aiming at the problem of low positioning accuracy of mixed sound source, a non iterative algorithm to complete cross spectral matrix is proposed, which uses the Hermitian characteristics of the cross-spectrum matrix without iteration and improves the computational efficiency without sacrificing positioning accuracy. This method first establishes a sparse model, and converts the source localization problem into a compressed sensing problem by constructing a redundant impulse response (RIR) matrix as a compressed sensing measurement matrix. Then, according to the spatial sparse correlation of multiple source direction vectors, a projection operator is introduced, and the root mean square error of azimuth is kept within 5% under the framework of compressed sensing. The simulation results in the uniform circular array (UCA) environment show that the algorithm has better estimation performance than the traditional algorithm.