To investigate the chemical abundance of broad-line region clouds in quasars at high redshifts, we performed near-infrared spectroscopy of six luminous quasars at z similar to 2.7 with the WINERED spectrograph mounted on the New Technology Telescope at the La Silla Observatory, Chile. The measured Fe ii/Mg ii flux ratios nearly matched with the published data for 0.7 less than or similar to z less than or similar to 1.6, suggesting that there is no evolution over a long period of cosmic time, which is consistent with previous studies. To derive the chemical abundances from the measured equivalent widths (EWs), their dependence on nonabundance factors must be corrected. In our previous paper, we proposed a method to derive the [Mg/Fe] abundance ratio and the [Fe/H] abundance by correcting the dependence of EW(Mg ii) and EW(Fe ii) on the Eddington ratio. To the best of our knowledge, that was the first report to discuss the star formation history through a direct comparison with chemical evolution models. In the present study, we further investigated the dependence of EWs on luminosity, which is known as the Baldwin effect (BEff). Additional correction for the BEff significantly affects the derived chemical abundances for the six luminous quasars at z similar to 2.7, and the resultant abundances agree well with the prediction of chemical evolution models. Given that most distant quasars found thus far are biased toward luminous ones, the correction of the measured EWs for the BEff is crucial for extending the chemical evolution study to higher redshifts.