Abstract – In this paper we propose an efficient method for a convex optimization problem which involves a large nonsymmetric and non-Toeplitz matrix. The proposed method is an instantiation of the alternating direction method of multipliers applied in Krylov subspace. Our method offers significant advantages in computational speed for the convex optimization problems involved with general matrices of large size. We apply the proposed method to the restoration of spatially variant blur. The matrix representing spatially variant blur is not block circulant with circulant blocks (BCCB). Efficient implementation based on diagonalization of BCCB matrices by the discrete Fourier transform is not applicable for spatially variant blur. Since the proposed method can efficiently work with general matrices, the restoration of spatially variant blur is a good application of our method. Experimental results for total variation restoration of spatially variant blur show that the proposed method provides meaningful solutions in a short time.