  Vector-like leptons (VLLs) as one kind of the most intriguing particles, have
been widely concerned in several extensions of the Standard Model (SM). In this
work, we explore the discovery potential of VLLs via pair production in the
context of models that satisfy asymptotic safety at the International Linear
Collider (ILC). The expected sensitivities of the ILC with the center of mass
energy $\sqrt{s} =$ 1 TeV and the integrated luminosity $\mathcal{L}$ = 1
ab$^{-1}$ to the parameter space of this kind of VLL models are derived. The
results we obtained show that, for the VLL with mass $M_F$ in the region of
$M_{F}\in$ [101GeV, 463GeV], the Yukawa coupling $\kappa $ can be as low as
$\kappa \in$ [0.032, 0.098].
