The objective of this study aims at selecting the most suitable supplier of Lithium-ion (Li-Ion) battery by the 2-tuple Fuzzy Linguistic Representation (FLR) model based on the Six Sigma- Define, Measure, Analyze, Improve and Control (DMAIC) processes. The fact that Li-Ion battery has several outstanding characteristics makes itself perfectly suited to today's high performance portable products. As a result, many suppliers have successively founded in several countries. Therefore, how to select a suitable Li-Ion battery supplier became a serious and important topic. This study is the first research on this topic. On the other hand, the motivation of proposing this decision process is twofold. One lies in its high precision setting on constructing the supplier selection framework through the Six Sigma DMAIC processes. The other is its superiority in providing aggregated outcomes for easy comparisons and analyses and in ensuring the consistent 2-tuple operations by introducing a geometric operator and a couple of new symbol translation functions. In case study, the world top ten Li-Ion battery suppliers are the candidates to be evaluated and selected. As results, a Japanese Li-Ion battery supplier is selected as the most suitable supplier. Several improvement suggestions are proposed according to analysis outcomes and can be used to develop the response plans for future performances.