<p>In this paper, an efficient algorithm is proposed for Toeplitz matrix recovery via hybrid thresholding operator. The algorithm is based on the mean-value augmented Lagrangian multiplier algorithm and the singular values are processed by hybrid singular value threshold operator. The new algorithm ensures that the matrix generated by the iteration has a Toeplitz structure, which reduces the calculation time and obtains a more accurate Toeplitz matrix. The convergence of the new algorithm is discussed under certain assumptions. Numerical experiments show that the new algorithm achieves lower CPU time than the mean-value augmented Lagrangian multiplier algorithm, smooth augmented Lagrangian multiplier algorithm, and augmented Lagrangian multiplier algorithm.</p>