DescriptionMGRIT re-discretize the problem with larger time-step width at the coarse-levels, which often cause unstable convergence. We propose a Krylov subspace method with MGRIT preconditioning as a more stable solver. For unstable problems, MGRIT preconditioned Krylov subspace method performed better than MGRIT in terms of the number of iterations. The contributions of the paper are organized as follows. We showed the matrix form of MGRIT operations, and the improvement of eigenvalue or singular-value distribution. We exemplified MGRIT with Krylov subspace method reaching convergence faster than MGRIT.