Let G be a graph of order n, and let a, b and k nonnegative integers with 2 ≤ a ≤ b. A graph G is called all fractional (a, b, k)-critical if after deleting any k vertices of G the remaining graph of G has all fractional [a, b]-factors. In this paper, it is proved that G is all fractional . Furthermore, it is shown that this result is best possible in some sense.