Sustainable material selection represents an important strategy in building design. Current building materials selection methods fail to provide adequate solutions for two major issues: assessment based on sustainability principles, and the process of prioritizing and assigning weights to relevant assessment criteria. This paper proposes a building material selection model based on the fuzzy extended analytical hierarchy process (FEAHP) techniques, with a view to providing solutions for these two issues. Assessment criteria are identified based on sustainable triple bottom line (TBL) approach and the need of building stakeholders. A questionnaire survey of building experts is conducted to assess the relative importance of the criteria and aggregate them into six independent assessment factors. The FEAHP is used to prioritize and assign important weightings for the identified criteria. A numerical example, illustrating the implementation of the model is given. The proposed model provides guidance to building designers in selecting sustainable building materials.