  While quasinormal modes of bosonic fields for the non-trivial $4$-dimensional
Einstein-Gauss-Bonnet theory of gravity suggested in [D.~Glavan and C.~Lin,
Phys.\ Rev.\ Lett.\ {\bf 124}, 081301 (2020)] have been recently studied, there
is no such study for fermionic fields. Here we calculate quasinormal modes of
the Dirac field for spherically symmetric asymptotically flat black hole in
this novel $4D$ Einstein-Gauss-Bonnet theory. The values of the quasinormal
frequencies, calculated by the 6th order WKB method with Pad\'{e} approximants
and the time-domain integration, show that the real part of the quasinormal
modes is considerably increased, while the damping rate is usually decreasing
when the coupling constant is growing.
