A line-depth ratio (LDR) of two spectral lines with different excitation potentials is expected to be correlated with the effective temperature (T_eff_). It is possible to determine T_eff_ of a star with a precision of tens of Kelvin if dozens or hundreds of tight LDR-T_eff_ relations can be used. Most of the previous studies on the LDR method were limited to optical wavelengths, but Taniguchi and collaborators reported 81 LDR relations in the YJ band, 0.97-1.32{mu}m, in 2018. However, with their sample of only 10 giants, it was impossible to account for the effects of surface gravity and metallicity on the LDRs well. Here, we investigate the gravity effect based on YJ-band spectra of 63 stars including dwarfs, giants, and supergiants observed with the WINERED spectrograph. We found that some LDR-T_eff_ relations show clear offsets between the sequence of dwarfs and those of giants/supergiants. The difference between the ionization potentials of the elements considered in each line pair and the corresponding difference in the depths can, at least partly, explain the dependency of the LDR on the surface gravity. In order to expand the stellar parameter ranges that the LDR method can cover with high precision, we obtained new sets of LDR-T_eff_ relations for solar-metal G0-K4 dwarfs and F7-K5 supergiants, respectively. The typical precision that can be achieved with our relations is 10-30K for both dwarfs and supergiants.