  The gradient flow exact renormalization group (GFERG) is an idea that
incorporates gauge invariant gradient flows into the formalism of the exact
renormalization group (ERG). GFERG introduces a Wilson action with a cutoff
while keeping vector gauge invariance manifestly. The details of the formalism
are still to be worked out. In this paper, we apply GFERG to construct the
Wilson action of massless Dirac fermions under the background chiral gauge
fields. By formulating the chiral anomaly as a ``composite operator,'' we make
the scale invariance of the anomaly manifest. We argue that the same result
extends to QCD.
