  In this paper, we investigate the driven dynamics of the localization
transition in the non-Hermitian Aubry-Andr\'{e} model with the periodic
boundary condition. Depending on the strength of the quasi-periodic potential
$\lambda$, this model undergoes a localization-delocalization phase transition.
We find that the localization length $\xi$ satisfies $\xi\sim
\varepsilon^{-\nu}$ with $\varepsilon$ being the distance from the critical
point and $\nu=1$ being a universal critical exponent independent of the
non-Hermitian parameter. In addition, from the finite-size scaling of the
energy gap between the ground state and the first excited state, we determine
the dynamic exponent $z$ as $z=2$. The critical exponent of the inverse
participation ratio (IPR) for the $n$th eigenstate is also determined as
$s=0.1197$. By changing $\varepsilon$ linearly to cross the critical point, we
find that the driven dynamics can be described by the Kibble-Zurek scaling
(KZS). Moreover, we show that the KZS with the same set of the exponents can be
generalized to the localization phase transitions in the excited states.
