Red quasars are very red in the optical through near-infrared (NIR) wavelengths, which is possibly due to dust extinction in their host galaxies as expected in a scenario in which red quasars are an intermediate population between merger-driven star-forming galaxies and unobscured type 1 quasars. However, alternative mechanisms also exist to explain their red colors: (i) an intrinsically red continuum; (ii) an unusual high covering factor of the hot dust component, that is, CF_HD = L_HD∕L_bol, where the L_HD is the luminosity from the hot dust component and the L_bol is the bolometric luminosity; and (iii) a moderate viewing angle. In order to investigate why red quasars are red, we studied optical and NIR spectra of 20 red quasars at z ~ 0.3 and 0.7, where the usage of the NIR spectra allowed us to look into red quasar properties in ways that are little affected by dust extinction. The Paschen to Balmer line ratios were derived for 13 red quasars and the values were found to be ~10 times higher than unobscured type 1 quasars, suggesting a heavy dust extinction with A_V > 2.5 mag. Furthermore, the Paschen to Balmer line ratios of red quasars are difficult to explain with plausible physical conditions without adopting the concept of the dust extinction. The CF_HD of red quasars are similar to, or marginally higher than, those of unobscured type 1 quasars. The Eddington ratios, computed for 19 out of 20 red quasars, are higher than those of unobscured type 1 quasars (by factors of 3−5), and hence the moderate viewing angle scenario is disfavored. Consequently, these results strongly suggest the dust extinction that is connected to an enhanced nuclear activity as the origin of the red color of red quasars, which is consistent with the merger-driven quasar evolution scenario.