The active galactic nucleus (AGN)-host co-evolution issue is investigated here by focusing on the evolution of the [O iii] λ5007 emission-line profile. A large sample of narrow emission-line galaxies is selected from the Max-Planck Institute for Astrophysics/Johns Hopkins University Sloan Digital Sky Survey DR7 catalog to simultaneously measure both the [O iii] line profile and circumnuclear stellar population in an individual spectrum. By requiring that (1) the [O iii] line signal-to-noise ratio is larger than 30 and (2) the [O iii] line width is larger than the instrumental resolution by a factor of two, our sample is narrowed down to 2333 Seyfert galaxies/LINERs (AGNs), 793 transition galaxies, and 190 star-forming galaxies. In addition to the commonly used profile parameters (i.e., line centroid, relative velocity shift, and velocity dispersion), two dimensionless shape parameters, skewness and kurtosis, are used to quantify the line shape deviation from a pure Gaussian function. We show that the transition galaxies are systematically associated with narrower line widths and weaker [O iii] broad wings than the AGNs, which implies that the kinematics of emission-line gas are different in the two kinds of objects. By combining the measured host properties and line shape parameters, we find that the AGNs with stronger blue asymmetries tend to be associated with younger stellar populations. However, a similar trend is not identified in the transition galaxies. The failure likely results from a selection effect in which the transition galaxies are systematically associated with younger stellar populations than the AGNs. The evolutionary significance revealed here suggests that both narrow-line region kinematics and outflow feedback in AGNs co-evolve with their host galaxies.