Purpose: A sustainable freight transportation system involves freight processes that are economically efficient, socially inclusive and environment friendly. For enhancing sustainability in the freight operations, mode selection is a crucial strategic decision. Therefore, the purpose of this paper is selecting the best mode, or a combination of modes based on various criteria to carry shipments from origin to destination. Design/methodology/approach: This study has used an integrated grey relational analysis based intuitionistic fuzzy multi-criteria decision-making process (GRA–IFP) and fuzzy multi-objective linear programming model. Three scenarios have been developed for analyzing sensitivity of decision variables with the variations in parameters under relevant conditions. A real case of Indian third-party logistics service provider has been used to demonstrate the effectiveness of the model. Findings: The most relevant criterion emerged out in this study for multi-mode selection problem is costs. It can be concluded from the study that multi-modal freight transportation has the potential to improve the sustainability of freight transportation by reducing the costs, damages, emissions, traffic congestion and by increasing the speed of delivering the shipment. The sensitivity analysis further shows that road is the economical mode, whereas sea and rail together are the greenest as well as socially responsible modes of transportation. Originality/value: This study provides an integrated tool, which can be used by freight transporters to decide upon the sustainable modes of transportation for their various shipments. © 2019, Emerald Publishing Limited.