We present an observed relationship between Eddington ratio ( \lambda _ { Edd } ) and optical narrow-emission-line ratio ( [ N ii ] \lambda 6583 /H \alpha ) of X-ray-selected broad-line active galactic nuclei ( AGN ) at 0.6 < z < 1.7 . We use 27 near-infrared spectra from the Fiber Multi-Object Spectrograph along with 26 sources from the literature . We show that the \lambda _ { Edd } and [ N ii ] \lambda 6583 /H \alpha ratio at 0.6 < z < 1.7 exhibits a similar anti-correlation distribution of \lambda _ { Edd } - [ N ii ] \lambda 6583 /H \alpha as has been found for local ( \langle z \rangle = 0.036 ) , ultra-hard X-ray selected AGN . The observed distribution implies that there is a consistent relationship from local to z \sim 1.7 which corresponds from the present time to 4 Gyr old . Further study of high redshift low Eddington ratio AGN ( { log } \lambda _ { Edd } < -2 ) is necessary to determine fully whether the \lambda _ { Edd } - [ N ii ] \lambda 6583 /H \alpha anti-correlation still holds in high-redshift AGN at low Eddington ratios .