Radar altimetry provides valuable measurements to characterize the state and the evolution of the ice sheet cover of Antartica and Greenland. Global Navigation Satellite System Reflectometry (GNSS-R) has the potential to complement the dedicated radar altimeters, increasing the temporal and spatial resolution of the measurements. Here we perform a study of the Greenland ice sheet using data obtained by the GNSS-R instrument aboard the British TechDemoSat-1 (TDS-1) satellite mission. TDS-1 was primarily designed to provide sea state information such as sea surface roughness or wind, but not altimetric products. The data have been analyzed with altimetric methodologies, already tested in aircraft based experiments, to extract signal delay observables to be used to infer properties of the Greenland ice sheet cover. The penetration depth of the GNSS signals into ice has also been considered. The large scale topographic signal obtained is consistent with the one obtained with ICEsat GLAS sensor, with differences likely to be related to L-band signal penetration into the ice and the along-track variations in structure and morphology of the firn and ice volumes The main conclusion derived from this work is that GNSS-R also provides potentially valuable measurements of the ice sheet cover. Thus, this methodology has the potential to complement our understanding of the ice firn and its evolution.