We report here results of spectropolarimetric observations of the classical T Tauri star (cTTS) GQ Lup carried out with ESPaDOnS at the Canada-France-Hawaii Telescope (CFHT) in the framework of the "Magnetic Protostars and Planets" (MaPP) programme, and obtained at 2 different epochs (2009 July & 2011 June). From these observations, we first infer that GQ Lup has a photospheric temperature of 4,300+-50\^A K and a rotation period of 8.4+-0.3 d; it implies that it is a 1.05+-0.07 Msun star viewed at an inclination of ~30deg, with an age of 2-5 Myr, a radius of 1.7+-0.2 Rsun, and has just started to develop a radiative core. Large Zeeman signatures are clearly detected at all times, both in photospheric lines & in accretion-powered emi...