Climate change mitigation is crucial to limit detrimental impacts of climate change on food production. However, cost-optimal mitigation pathways consistent with the Paris agreement project large-scale land-based mitigation for bio-energy and afforestation to achieve stringent climate targets. Land demand from land-based mitigation leads to competition with food production, raising concerns that climate policy (SDG13 climate action) conflicts with food security objectives (SDG2 zero hunger). In this study we use the computable general equilibrium model MAGNET and the IMAGE integrated assessment model to quantify the food security effects of large-scale land-based mitigation. Subsequently, we implement two measures to prevent reduced food security: increased agricultural intensification and reduced meat consumption. We show that large-scale land-based mitigation (600 Mha in 2050) leads to increased food prices (11), reduced food availability (230 kcal/cap/day) and substantially more people at risk of hunger (230 million) compared to the baseline scenario in 2050, most notably in developing regions. Land-based mitigation also leads to yield increases (9) and intensified ruminant production (11). Additional crop yield improvement (9) and intensification in ruminant production (3) could prevent the negative effect of mitigation on food security. Introducing a reduction in meat consumption in high- and middle-income regions reduces required crop yield improvement (7) and ruminant intensification (2). Our study highlights the importance of transparency about food security effects in climate change mitigation scenarios. In addition, it provides an example of explicitly including measures to limit negative trade-offs in mitigation scenarios. In this way, we show how the Paris agreement can be made consistent with food security objectives and how multiple Sustainable Development Goals can be achieved.