We present a detailed study of the stars of the NASA InfraRed Telescope Facility (IRTF) spectral library to understand its full extent and reliability for use with stellar population (SP) modeling. The library consist of 210 stars, with a total of 292 spectra, covering the wavelength range of 0.94 to 2.41 μm at a resolution R ≈ 2000. For every star we infer the effective temperature (Teff), gravity (log g) and metallicity ([Z/Z⊙]) using a full-spectrum fitting approach in a section of the K-band (2.19 to 2.34 μm) and temperature-NIR colour relations. We test the flux calibration of these stars by calculating their integrated colours and comparing them with the Pickles library colour-temperature relations. We also investigate the NIR colours as a function of the calculated effective temperature and compared them in colour-colour diagrams with the Pickles library. This latter test shows a good broad-band flux calibration, important for the SP models. Finally, we measure the resolution R as a function of wavelength. We find that the resolution increases as a function of lambda from about 6 Å in J to 10 Å in the red part of the K-band. With these tests we establish that the IRTF library, the largest currently available general library of stars at intermediate resolution in the NIR, is an excellent candidate to be used in stellar population models. We present these models in the next paper of this series. The IRTF spectral library is available at irtfweb.ifa.hawaii.edu/spex/IRTF_Spectral_Library/