  We investigate the evolution of entanglement spectra under a global quantum
quench from a short-range correlated state to the quantum critical point.
Motivated by the conformal mapping, we find that the dynamical entanglement
spectra demonstrate distinct finite-size scaling behaviors from the static
case. As a prototypical example, we compute real-time dynamics of the
entanglement spectra of a one-dimensional transverse-field Ising chain.
Numerical simulation confirms that, the entanglement spectra scale with the
subsystem size $l$ as $\sim l^{-1}$ for the dynamical equilibrium state, much
faster than $\propto \log^{-1} l$ for the critical ground state. In particular,
as a byproduct, the entanglement spectra at the long time limit faithfully
gives universal tower structure of underlying Ising criticality, which shows
the emergence of operator-state correspondence in the quantum dynamics.
