An efficient multigrid diagonalized ADI(DADI) method for the compressible flows is presented. The second-order upwind TV13 scheme in conjecture with the Roe`s flux-difference splitting(FDS) is used for the numerical flux function. An implicit operator, which is consistent with the Roe`s FDS, is derived from the numerical flux. A modified saw-tooth cycle multigrid method is developed to accelerate residual propagation.To verify the efficiency of the present method, 2-13 and 3-13 transonic flows are computed and comparisons with the explicit method with the multigrid are presented. The comparisons with the multigrid explicit method show that the present scheme can obtain the same numerical result within only 10% of computing cost. TI-ie comparison with the results of single grid DADI reveals that the convergence can be accelerated by a factor of 3-7 by the present multigrid method.