A significant 'size effect' is observed in ice failure strength: the ice strength is not independent of ice fragment size, but decreases with increasing size. The fractal approach to the ice mechanics with a multiscale microstructure provides an elegant and unified explanation of the size effect on ice failure strength. Ice fragments are found to have a fractal size distribution, with a fractal dimension (D) close to 2.50 over a remarkably wide range of ice fragment size. The size effect on ice strength can be well predicted using the fractal dimension D=2.50 of the ice fragment size distribution.