Data envelopment analysis (DEA) is a popular technique for evaluating relative efficiency. In many real-world applications, undesirable outputs must be considered, and evaluating eco-efficiency instead of operational efficiency is demanded. Unfortunately, eco-efficiency models in DEA are problematic, especially in variable returns-to-scale (VRS) and weak disposability conditions. In this paper, the shortcomings of the available models are discussed and a new method is proposed to provide a valid eco-efficiency measurement. The proposed model is capable of assessing radial efficiency which is not straightforward in the presence of undesirable outputs. Weak disposability condition plays an important role in modelling undesirable outputs. The proposed model also offers a new formulation for weak disposability in VRS technology. Compared to conventional DEA models with a large number of decision making units evaluated as efficient, the performance scores in the proposed model are much more dispersed, leading to a deeper assessment. None of the operational and environmental efficiencies is overlooked by the new method. The proposed model is used to evaluate the eco-efficiency of the agriculture sector in 62 countries. The results confirm that poverty and extreme weather have negative impacts on environmental efficiency.