Supplier selection is one of the most important activities of purchasing departments. This importance is increased even more by new strategies in a supply chain, because of the key role suppliers perform in terms of quality, costs and services which affect the outcome in the buyer’s company. Supplier selection is a multiple criteria decision making problem in which the objectives are not equally important. In practice, vagueness and imprecision of the goals, constraints and parameters in this problem make the decision making complicated. Simultaneously, in this model, vagueness of input data and varying importance of criteria are considered. In real cases, where Decision- Makers (DMs) face up to uncertain data and situations, the proposed model can help DMs to find out the appropriate ordering from each supplier, and allows purchasing manager(s) to manage supply chain performance on cost, quality, on time delivery, etc. An additive weighted model is presented for fuzzy multi objective supplier selection problem with fuzzy weights. The model is explained by an illustrative example.