  We investigate an interacting supersymmetric gradient flow in the Wess-Zumino
model. Thanks to the nonrenormalization theorem and an appropriate initial
condition, we find that any correlator of flowed fields is ultraviolet finite.
This is shown at all orders of the perturbation theory using the power counting
theorem for one-particle irreducible supergraphs. Since the model does not have
the gauge symmetry, the mechanism of realizing the ultraviolet finiteness is
quite different from that of the Yang-Mills flow, and this could provide
further understanding of the gradient flow approach.
