Increasing societal demand for a more ecological agriculture stimulates demand for farm management systems adapted to non-standard situations such as low-nitrogen systems. However, trade-offs between traits of interest could make difficult to reach high agronomic and environment performances. For malting barley, premium prices depend on grain protein content and grain size with strong trade-offs with yield, such traits being highly dependent on practices and genotypes. Here we assume that such trade-offs can be implicitly embedded in models taking into account varietal traits. Starting with an existing wheat-crop model, we developed a parsimonious barley-crop model on how genotypic traits, crop management practices and pedo-climatic environment determine yield, grain protein content and grain size. Grain size predictions required the development of a new module. We parameterized the model with published and new experimental data using 200 genotype-by-environment combinations of high- and low-input management situations. The model was then assessed on 280 other situations, including high and low level of nitrogen input. The relative root mean square error of prediction of the model on hold-out data was below 15% for grain yield, grain protein content and grain retention fraction in high and low-input situations. In addition, the model correctly ranked 72% of the genotype pairs for grain yield, 55% for grain protein content and 85% for grain retention fraction. Our model can be used to predict grain protein content and retention fraction, and rank yield and calibrated yield performance of existing combinations of genotype by management by environment combinations. It also could help to explore new combinations, to support breeding.