Decision support tools to help dairy farmers gain confidence in grazing management need to be able to predict performance of grazing animals with easy-to-obtain variables on farm. This paper, the second of a series of three, describes the GrazeIn model predicting herbage intake for grazing dairy cows. The model of voluntary intake described in the first paper is adapted to grazing situations taking account of sward characteristics and grazing management, which can potentially affect intake compared to indoor feeding. Rotational and continuously stocked grazing systems are considered separately. Specific effects of grazing management on intake were quantified from an extensive literature review, including the effect of daily herbage allowance and pre-grazing herbage mass in rotational grazing systems, sward surface height in continuously stocked grazing systems, and daily time at pasture in both grazing systems. The model, based on iterative procedures, estimates many interactions between cows, supplements, sward characteristics and grazing management. The sensitivity of the prediction of herbage intake to sward and management characteristics, as well as the robustness of the simulations and an external validation of the GrazeIn model with an independent data set, is presented in a third paper.