The goals of sustainable development are constantly negatively impacted by infrastructure initiatives. The importance of these projects in advancing the economic, social, and civilizational growth of the country will, however, prevent their construction from being stopped. The overall construction of the project is related to the scientific and unbiased assessment of an infrastructure project’s sustainability throughout the decision-making stage. Based on the references documents, this paper establishes an index system for evaluating an infrastructure project’s sustainability from three aspects: environment, economy, and society. In the assessment process, the cloud model was used to describe the various attribute values of infrastructure project sustainability, which achieved the uncertainty measures for infrastructure project sustainability, and a cloud model-based assessment method for infrastructure project sustainability was proposed by modifying the attribute value by the penalty factor. Finally, an assessment method for infrastructure project sustainability based on the cloud model was proposed after the attribute values were modified by using a continuous interval argument ordered weighted average (C-OWA) operator. The model carries out an overall sustainability assessment by generating a synthesized cloud with the weight to calculate the similarity of assessment factors, which takes the randomness, fuzziness, and uncertainty of expert qualitative assessment into account, and uses the analytic hierarchy process (AHP) method and the C-OWA operator to determine the weight of the sustainable index and the aggregation of the expert scoring interval. A case study was conducted to clarify how this strategy was applied. The study provides a valuable and useful tool for the operational stage to assess the achievability of municipal infrastructure projects.