The climate crisis is urging us to act fast. Buildings are a key leverage point to reduce greenhouse gas (GHG) emissions, but the embodied emissions related with their construction remain often the hidden challenge of any ambitious policy. Since a complete material substitution is not possible, we explore in this paper a material greenhouse gas (GHG) compensation where fast growing bio-based insulation materials are used to compensate building elements which necessarily release GHG. Different material diets as well as different building typologies are modelled to assess the consequences in term of bio-based insulation requirement to reach climate-neutrality. Our results show that it is possible to build climate-neutral buildings with sufficient energy performance to fulfil current standards and with building components thickness within the range of current construction practices. This paper evidences that it is technically feasible and that climate-neutrality in construction sector without a radical technology breakthrough.