Science Verification observations with the High Acuity Wide field K-band Imager (HAWK-I) instrument enhanced by the ground-layer adaptive optics module (GRAAL) were obtained during 4.5 nights from 2 to 6 January 2018. Fourteen projects were selected from a total of 19 submitted proposals. The total time scheduled for these 14 projects was 35.5 hours, which represents a slight oversubscription for the four allocated summer nights. The seven top- ranked projects were completed, three more programmes received some data, one was observed outside the requested constraints, and three projects were not started. The Science Verification nights were affected by various technical problems, mostly unrelated to GRAAL, which resulted in a total loss of 10 hours. Half a night was allocated on 6 January to compensate for some of the lost time. The atmospheric conditions were rather variable with occasionally excellent natural seeing (0.3 arcseconds). The ground layer turbulence fraction varied from 40% to 85% during these nights. The best performance in terms of improved image quality was observed when the ground layer fraction was above 70%, as expected for the system. The image quality in the K filter ranged between 0.2 arcseconds (in excellent conditions) to about 0.5 arcseconds (with mediocre seeing, > 0.8 arcseconds), and a small fraction of ground-layer turbulence. The delivered image quality was very stable, but in some cases an asymmetric point spread function was observed.