We present new JHK spectroscopy (R ~ 5000) of GQ Lup b, acquired with the near-infrared integral field spectrograph NIFS and the adaptive optics system ALTAIR at the Gemini North telescope. Angular differential imaging was used in the J and H bands to suppress the speckle noise from GQ Lup A; we show that this approach can provide improvements in signal-to-noise ratio (S/N) by a factor of 2 - 6 for companions located at subarcsecond separations. Based on high quality observations and GAIA synthetic spectra, we estimate the companion effective temperature to Teff = 2400 +/- 100 K, its gravity to log g = 4.0 +/- 0.5, and its luminosity to log(L/L_s) = -2.47 +/- 0.28. Comparisons with the predictions of the DUSTY evolutionary tracks allow us to constrain the mass of GQ Lup b to 8 - 60 MJup, most likely in the brown dwarf regime. Compared with the spectra published by Seifahrt and collaborators, our spectra of GQ Lup b are significantly redder (by 15 - 50%) and do not show important Pabeta emission. Our spectra are in excellent agreement with the lower S/N spectra previously published by McElwain and collaborators.