  The two-loop self-energy correction is evaluated to all orders in Z\alpha for
the ground-state Lamb shift of H-like ions with Z >= 10, where Z is the nuclear
charge number and \alpha is the fine structure constant. The results obtained
are compared with the analytical values for the Z\alpha-expansion coefficients.
An extrapolation of the all-order numerical results to Z=1 is presented and
implications of our calculation for the hydrogen Lamb shift are discussed.
