Livestock products and the sustainability of their production process play an important role in food security, value addition, job creation, and the growth of related industries. Therefore, this paper was organized to evaluate the sustainability situation in the livestock supply chain in Pasargad City by introducing a new sustainability index. The economic, social, and environmental conditions of the livestock supply chain by using data were collected by completing two types of questionnaires on the status of light and heavy livestock evaluated. The results obtained using the analytical hierarchy process method showed that in this case, the economic criterion is more important than the social and environmental. For financial evaluation, the indices of benefit–cost ratio, net profit, and return on capital were calculated. The employment status and the level of the social status of the producers were evaluated. In the environmental assessment, the amount of greenhouse gas emissions for the production and consumption of feed used by livestock and transportation of inputs and products in the production process was calculated. The production of both light and heavy livestock has economic justification, but, in terms of environmental evaluation, light livestock, and, in terms of social evaluation, heavy livestock are preferable. Therefore, based on the calculation of the sustainability index, the beef supply chain is prioritized. Investment and special support regarding the establishment of a milk processing factory and industrial slaughterhouse in Pasargad City to increase sustainability in the supply chain of livestock products is suggested.