  We apply the functional renormalization group approach to a $\mathcal{N}=1$
supersymmetric gauge model with one chiral superfield coupled to a vector
$U(1)$ superfield. We find that the nonrenormalization theorem still works at
leading order in the supercovariant derivative expansion of the fields. We also
find the beta functions and we study the behavior of its fixed points in the
local potential approximation. Regulators are also discussed.
