  In K.~Hieda, A.~Kasai, H.~Makino, and H.~Suzuki, Prog.\ Theor.\ Exp.\ Phys.\
\textbf{2017}, 063B03 (2017), a properly normalized supercurrent in the
four-dimensional (4D) $\mathcal{N}=1$ super Yang--Mills theory (SYM) that works
within on-mass-shell correlation functions of gauge-invariant operators is
expressed in a regularization-independent manner by employing the gradient
flow. In the present paper, this construction is extended to the supercurrent
in the 4D $\mathcal{N}=2$ SYM. The so-constructed supercurrent will be useful,
for instance, for fine tuning of lattice parameters toward the supersymmetric
continuum limit in future lattice simulations of the 4D $\mathcal{N}=2$ SYM.
