Materials constitute a large proportion of the total project cost and the absence of right materials in the right quantities and quality on site when needed is one of the most commonly experienced causes of delays in construction projects. Although supplier selection is a strategic issue, contractors generally select suppliers based on their past experiences, which may result in selecting wrong suppliers. Supplier selection decision is generally made by multiple decision makers and is affected by several criteria. Therefore, selecting the right supplier among many alternatives considering several compromising and conflicting criteria is a multi-criteria group decision-making (MCGDM) problem. This paper proposes an integrated fuzzy MCGDM approach, which employs fuzzy analytic hierarchy process (AHP) and fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) together, for the supplier selection problem. In the proposed approach, fuzzy AHP is used to analyse the structure of the supplier selection problem and to determine the weights of the criteria, and the fuzzy TOPSIS method is employed to rank the alternative suppliers. The proposed approach is applied to a problem of selecting the most appropriate rail supplier and company management found the proposed decision approach satisfactory and implementable in future supplier selection problems.