Lean Six Sigma (LSS) aims to assist enterprises in improving the production process, quality, efficiency and effective status, and is regarded as the latest trend in Six Sigma. The purpose of the paper is to build the LSS framework and show how to use LSS to reduce the stock cost. To achieve the research objectives, the paper reviewed the literature on LSS. By integrating Six Sigma DMAIC implementation with the lean concept, the three inventory models (basic fixed-order-quantity model, Economic Order Quantity (EOQ) model and two-bin approach) are compared with regard to reducing stock cost in a case study of Taiwanese enterprises which were able to develop and judge the LSS that best allocates organizational resources to solve this critical business problem. The EOQ model has better inventory management and is thus able to reduce the stock cost better. The organization may depend on off season and busy season demand to judge what EOQ quantity to purchase, and this EOQ model can effectively control the stock cost and meet the improvement goals of LSS. The value of the paper lies in its observation of the improvement steps following LSS implementation. It is also found that as a strategy-oriented initiative of LSS, Six Sigma activities must be adapted and modified to fit the lean management environment.