  $\mathcal{PT}$ symmetry, that is, a combined parity and time-reversal
symmetry is a key milestone for non-Hermite systems exhibiting entirely real
eigenenergy. In the present work, motivated by a recent experiment, we study
$\mathcal{PT}$ symmetry of the time-evolution operator of non-unitary quantum
walks. We present the explicit definition of $\mathcal{PT}$ symmetry by
employing a concept of symmetry time frames. We provide a necessary and
sufficient condition so that the time-evolution operator of the non-unitary
quantum walk retains $\mathcal{PT}$ symmetry even when parameters of the model
depend on position. It is also shown that there exist extra symmetries embedded
in the time-evolution operator. Applying these results, we clarify that the
non-unitary quantum walk in the experiment does have $\mathcal{PT}$ symmetry.
