  $\mathcal{PT}$ symmetry, namely, a combined parity and time-reversal symmetry
can make non-unitary quantum walks exhibit entirely real eigenenergy. However,
it is known that the concept of $\mathcal{PT}$ symmetry can be generalized and
an arbitrary anti-unitary symmetry has a possibility to substitute
$\mathcal{PT}$ symmetry. The aim of the present work is to seek such
non-unitary quantum walks with generalized $\mathcal{PT}$ symmetry by focusing
on effects of spatially random disorder which breaks $\mathcal{PT}$ symmetry.
We numerically find non-unitary quantum walks whose quasi-energy is entirely
real despite $\mathcal{PT}$ symmetry is broken.
