The aim of this study was to investigate the effects of increasing amounts of cereal-based concentrate on milk production. The study consisted of a series of three separate experiments in which cows were grazed in intensive rotation on timothy-meadow fescue pasture. In Experiment 1, 28 multiparous Holstein–Friesian cows received 0, 3, 6 and 9 kg concentrate in a cross-over designed trial with a fixed daily herbage allowance of 21 kg DM/cow. The energy-corrected milk yield increased linearly 0.84 kg/kg DM (P < 0.001), up to the 9 kg concentrate level. The milk fat (P < 0.001) and urea (P < 0.001) content decreased linearly (0.41 g/kg DM and 0.15 mmol/kg DM, respectively). The milk protein content tended (P = 0.08) to increase 0.10 g/kg DM with increasing supplementation. In Experiment 2, 17 primiparous cows and 28 multiparous cows were used in a randomized-block designed trial with 3, 6 and 9 kg concentrate supplementation and a fixed 25 kg DM herbage allowance. The energy corrected milk yield increased linearly (P < 0.01) 0.67 kg/kg DM, whereas the milk urea content decreased linearly (P < 0.001) 0.27 mmol/kg DM. The milk protein content increased and the fat content decreased, but these differences were not significant. In Experiment 3, a cross-over design was used to assess the response to concentrate supplementation of 24 multiparous cows (treatments: 6, 9 and 12 kg; fixed herbage allowance 25 kg DM) and 12 primiparous cows (treatments: 4, 7 and 10 kg; herbage allowance > 25 kg DM). The energy-corrected milk yield of the multiparous cows varied quadratically (Pquad < 0.001; 30.0, 32.5 and 32.2 kg for 6, 9 and 12 kg supplementation, respectively). Supplementation linearly decreased the urea (P < 0.001) 0.13 mmol/kg DM and fat (P < 0.001) 0.46 g/kg DM contents. The milk fat content also varied quadratically, showing the lowest content with the 12 kg level (Pquad < 0.05; 37.3, 37.3 and 34.9 g/kg for 6, 9 and 12 kg supplementation, respectively). The energy-corrected milk yield of the primiparous cows increased linearly (P < 0.001) 0.54 kg/kg DM up to 10 kg supplementation, whereas the milk urea (P < 0.001) and fat contents decreased linearly (P < 0.01) by 0.19 mmol/kg DM and 0.61 g/kg DM, respectively. The results showed that the milk response remained linear up to the 9 kg supplementation level, but the highest level of supplementation resulted in only a marginal increase in milk yield. There was no interaction between season and milk or milk protein yield, which indicates that it is possible to maintain stable grazing conditions during the main grazing season in Nordic latitudes. The results support to some extent the hypothesis that the marginal milk response to supplementation increases with increasing milk production.