We study the time evolution of the chirality imbalance n5 and the chiral magnetic effect (CME) under the external parallel electromagnetic (EM) 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 n5 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 n5 and the fermion pair-production rate from the vacuum. We also discuss the dynamical origin of the chirality imbalance in detail.