As ruminants are able to digest fibre efficiently and assuming that competition for feed v. food use would intensify in the future, cereals and other field crops should primarily be destined to cover the dietary needs of humans and monogastric animals such as poultry and pigs. Farming systems with a reduced or absent concentrate supplementation, as postulated by organic agriculture associations, require adapted dairy cows. The aim of this experiment was to examine the impact of concentrate supplementation on milk production, grazing and rumination behaviour, feed intake, physical activity and blood traits with two Holstein-Friesian cow strains and to conclude the consequences for sustainable and organic farming. The experiment was a cross-over study and took place on an organic farm in Switzerland. In all, 12 Swiss Holstein-Friesian (HCH) cows and 12 New Zealand Holstein-Friesian (HNZ) cows, which were paired according to lactation number, days in milk and age for primiparous cows, were used. All cows grazed full time and were supplemented either with 6 kg/day of a commercial, organic cereal-grain mix or received no supplement. After an adaptation period of 21 days, a measurement period of 7 days followed, where milk yield and composition, pasture dry matter intake estimated with the n-alkane double-indicator technique, physical activity based on pedometer measurements, grazing behaviour recorded by automatic jaw movement recorder and blood samples were investigated. Non-supplemented cows had a lower milk yield and supplemented HCH cows produced more milk than supplemented HNZ cows. Grazing time and physical activity were greater for non-supplemented cows. Supplementation had no effect on rumination behaviour, but HNZ cows spent longer ruminating compared with HCH cows. Pasture dry matter intake decreased with the concentrate supplementation. Results of blood analysis did not indicate a strong negative energy balance for either non-supplemented or supplemented cows. Minor differences between cow strains in this short-term study indicated that both cow strains are equally suited for an organic pasture-based production system with no concentrate supplementation. Many factors such as milk yield potential, animal welfare and health, efficiency, grazing behaviour and social aspects influence the decision to supplement grazing dairy cows with concentrates.