This paper proposes a new index for assessing sustainability of the industrial sector i.e. the Industrial Sustainability Index (ISI) and demonstrates its utility by applying it to an energy intensive industry. The proposed index incorporates all the three major dimensions of sustainability viz. economic, environmental, and social. It represents the socio-economic benefit of an industry per unit of its carbon emissions. The specific energy consumption or energy intensity (with commensurate carbon emissions), which is usually reported as a measure of environmental impact of various industries, does not include the social and economic parameters. The proposed ISI also overcomes the difficulties in assessing specific energy consumption such as allocation in case of multiple products and its variability with the type and scale of production. To illustrate, the proposed index has been evaluated for a typical paper industry in India. Further, opportunities for its improvement by fuel substitution and repowering through combined cycle power generation have been examined. With existing ISI of 16 units to an improved ISI of 78 units, approximately five times improvement in ISI was observed, indicating a potential for significant improvement in industrial sustainability through such measures.