Discussions on climate change increasingly emphasize the contribution of agricultural activities to anthropogenic greenhouse gases emissions. In this paper, we investigate from a supply to demand side perspective the stress between food demand and climate change challenges up until 2030. We examine how more stringent climate change mitigation policies could alter agricultural markets and put at risk the nutrition possibilities of populations. We use for this purpose GLOBIOM, an applied partial equilibrium model covering, at the world scale and a fine grid resolution, the main land-based sectors: agriculture, forestry and bioenergy. For this exercise, the model is fully linked to a semi-flexible endogenous demand system with non-linear Engel’s curves. Our results show that although forest related measures could be efficiently deployed without harming food security, a scenario of massive development of bioenergy would have more tangible impacts on food availability. Our most constraining option is a decrease in emissions from cattle, which would impose a reduction in the consumption of ruminant meat and milk. We illustrate that considering the current dynamic of consumption patterns, these latter policies, if implemented on the supply side directly, could have very uneven effects to the world’s diet and harm primarily developing countries.