Thanks to the recent very high precision photometry of red giants from satellites such as Kepler, precise mass and radius values as well as accurate information of evolutionary stages are already established by asteroseismic approach for a large number of G-K giants. Based on the high-dispersion spectra of selected such 55 red giants in the Kepler field with precisely known seismic parameters (among which parallaxes are available for nine stars), we checked the accuracy of the determination method of stellar parameters previously applied to many red giants by Takeda et al. (2008PASJ...60..781T), since it may be possible to discriminate their complex evolutionary status by using the surface gravity versus mass diagram. We confirmed that our spectroscopic gravity and the seismic gravity satisfactorily agree with each other (to within ~0.1 dex) without any systematic difference. However, the mass values of He-burning red clump giants derived from stellar evolutionary tracks (~2-3 M_{sun}_) were found to be markedly larger by ~50 percent compared to the seismic values (~1-2 M_{sun}_) though such discrepancy is not seen for normal giants in the H-burning phase, which reflects the difficulty of mass determination from intricately overlapping tracks on the luminosity versus effective temperature diagram. This consequence implies that the mass results of many red giants in the clump region determined by Takeda et al. are likely to be significantly overestimated. We also compare our spectroscopically established parameters with recent literature values, and further discuss the prospect of distinguishing the evolutionary status of red giants based on the conventional (i.e. non-seismic) approach.