One percent of redshift z ∼ 0.1 Active Galactic Nuclei (AGNs) show velocity splitting of a few hundred km s −1 in the narrow emission lines in spatially integrated spectra. Such line profiles have been found to arise from the bulk motion of ionized gas clouds associated with galactic-scale outflows, merging pairs of galaxies each harboring a supermassive black hole (SMBH), and/or galactic-scale disk rotation. It remains unclear, however, how the frequency of narrow-line velocity splitting may depend on AGN luminosity. Here we study the correlation between the fraction of Type 2 AGNs with double-peaked narrow emission lines and AGN luminosity as indicated by. We combine the sample of Liu et al. (2010a) at z ∼ 0.1 with a new sample of 178 Type 2 AGNs with double-peaked [O iii] emission lines at z ∼ 0.5. We select the new sample from a parent sample of 2089 Type 2 AGNs from the SDSS-III/Baryon Oscillation Spectroscopic Survey. We find a statistically significant (∼ 4.2σ) correlation between L [O iii] and the fraction of objects that exhibit double-peaked narrow emission lines among all Type 2 AGNs, corrected for selection bias and incompleteness due to [O iii] line width, equivalent width, splitting velocity, and/or equivalent width ratio between the two velocity components. Our result suggests that galactic-scale outflows and/or merging pairs of SMBHs are more prevalent in more powerful AGNs, although spatially resolved follow up observations are needed to resolve the origin(s) for the narrow-line velocity splitting for individual AGNs.