Increased economic, societal and environmental challenges facing agriculture are leading to a greater focus on effective way to combine grazing and automatic milking systems (AMS). One of the fundamental aspects of robotic milking is cows' traffic to the AMS. Numerous studies have identified feed provided, either as fresh grass or concentrate supplement, as the main incentive for cows to return to the robot. The aim of this study was to determine the effect of concentrate allocation on voluntary cow traffic from pasture to the robot during the grazing period, to highlight the interactions between grazed pasture and concentrate allocation in terms of substitution rate and the subsequent effect on average milk yield and composition. Thus, 29 grazing cows, milked by a mobile robot, were monitored for the grazing period (4 months). They were assigned to two groups: a low concentrate (LC) group (15 cows) and a high concentrate (HC) group (14 cows) receiving 2 and 4 kg concentrate/cow per day, respectively; two allocations per day of fresh pasture were provided at 0700 and 1600 h. The cows had to go through the AMS to receive the fresh pasture allocation. The effect of concentrate level on robot visitation was calculated by summing milkings, refusals and failed milkings/cow per day. The impact on average daily milk yield and composition was also determined. The interaction between lactation number and month was used as an indicator of pasture availability. Concentrate allocation increased significantly robot visitations in HC (3.60 ± 0.07 visitations/cow per day in HC and 3.10 ± 0.07 visitations/cow per day in LC; P < 0.001) while milkings/cow per day were similar in both groups (LC: 2.37 ± 0.02/day and HC: 2.39 ± 0.02/day; Ns). The average daily milk yield over the grazing period was enhanced in HC (22.39 ± 0.22 kg/cow per day in HC and 21.33 ± 0.22 kg/cow per day in LC; P < 0.001). However the gain in milk due to higher concentrate supply was limited with regards to the amount of provided concentrates. Milking frequency in HC primiparous compared with LC was increased. In the context of this study, considering high concentrate levels as an incentive for robot visitation might be questioned, as it had no impact on milking frequency and limited impact on average milk yield and composition. By contrast, increased concentrate supply could be targeted specifically to primiparous cows.