We present rest-frame optical spectra of 12 nitrogen-loud quasars at z ~ 2.2, whose rest-frame ultraviolet (UV) spectra show strong nitrogen broad emission lines. To investigate their narrow-line region (NLR) metallicities, we measure the equivalent width (EW) of the [OIII]5007 emission line: if the NLR metallicity is remarkably high as suggested by strong UV nitrogen lines, the [OIII]5007 line flux should be very week due to the low equilibrium temperature of the ionized gas owing to significant metal cooling. In the result, we found that our spectra show moderate EW of the [OIII]5007 line similar to general quasars. This indicates nitrogen-loud quasars do not have extremely metal-rich gas clouds in NLRs. This suggests that strong nitrogen lines from broad-line regions (BLRs) are originated by exceptionally high abundances of nitrogen relative to oxygen without very high BLR metallicities. This result indicates that broad-emission lines of nitrogen are not good indicators of the BLR metallicity in some cases. On the other hand, we also investigate virial black-hole masses and Eddington ratios by using the Hbeta and CIV1549 lines for our sample. As a result, we found that black-hole masses and Eddington ratios of nitrogen-loud quasars tend to be low and high relative to normal quasars, suggesting that nitrogen-loud quasars seem to be in a rapidly-accreting phase. This can be explained in terms of a positive correlation between Eddington ratios and nitrogen abundances of quasars, that is probably caused by the connection between the mass accretion onto black holes and nuclear star formation.