  We study the time evolution of the chirality imbalance $n_5$ and the chiral
magnetic effect (CME) under the external parallel electromagnetic fields
without assuming the artificial chiral asymmetric source. We adopt the
time-dependent Sauter-type electric and constant magnetic field, and obtain
analytical solutions of the Dirac equation for a massive fermion. We use the
point-split regularization to calculate the vacuum contribution in the gauge
invariant way. As a result, we find that $n_5$ and CME current increase
substantially as the electric field increases, and stay finite after the
electric field is switched off. The chirality imbalance and CME current are
shown to consist of a dominant contribution, which is essentially proportional
to relativistic velocity, and a small oscillating part. We find a simple
analytical relation between $n_5$ and the fermion pair-production rate from the
vacuum. We also discuss dynamical origin of the chirality imbalance in detail.
