We present long-slit near-infrared spectroscopic observations of six nearby (z~0.1) radio-quiet type-2 quasars (QSO2s) from the Quasar Feedback (QSOFEED) sample. They have bolometric luminosities of 10^{45-46} erg/s and stellar masses of 10^{10.6-11.3} Msun. The observations were obtained with the instrument Espectrógrafo Multiobjeto Infra-Rojo (EMIR) on the 10.4 m Gran Telescopio Canarias. The nuclear K-band spectra (central ~1-3 kpc of the QSO2s) reveal signatures of high-velocity outflows in either the Pa\alpha or Br\gamma lines, depending on the redshift, and in the [Si VI] lines. The broadest kinematic components have full width at half maximum (FWHM) of ~1200-2500 km/s. From the near-infrared hydrogen recombination lines we derived ionized outflow masses of M_Hion ~0.08-20x10^6 Msun, mass outflow rates of ~0.03-6~Msun/yr, and kinetic powers of ~10^{37.8-40.8} erg/s. These ionized gas outflow masses and mass outflow rates have median values that are 5.9 and 5.8 times larger, respectively, than those derived from the [Si VI] line. Our study provides evidence, at least for these six QSO2s, that the near-infrared recombination lines and [Si VI] are tracing the same outflow (i.e., they have similar kinematics and radii), but they carry different amounts of mass. We detected warm molecular lines in the six QSO2s, from which we measured total (nuclear) gas masses from 1.1 (0.7) to 32 (13) x10^3 Msun, similar to other QSO2s with warm H_2 measurements reported in the literature, but we did not find any molecular outflow associated with them. Comparing with other five QSO2s with H_2 measurements reported in the literature, we find that the four QSO2s with detected H_2 outflows have total (nuclear) H_2 masses 2.2 (2.7) times larger, on average.