We present new mid-resolution (R=2000-4000) near infrared (JHK) spectra of the substellar companion to GQ Lup, taken with the integral-field spectrograph SINFONI at the VLT. The GQ Lup companion is a low-mass proper-motion companion to the 1(+/-1) Myr old T-Tauri star GQ Lup A and is supposedly of planetary mass according to recent theoretical models. We compare the measured spectra with the newest generation of synthetic PHOENIX spectra and derive new limits on Teff and logg, which in turn allows a more precise mass determination of the GQ Lup companion.