Employment of a systematic approach for prioritization of improvement projects and addressing the voice of the stakeholders are imperative for organizations in the current business circumstances. This study suggests a novel approach that employs multi-criteria decision-making (MCDM) methods for project prioritization. A combination of step-wise weight assessment ratio analysis (SWARA) method and house of quality (HOQ) is used in the calculation of the importance of criteria, followed by utilization of criteria importance in COmplex PRoportional ASsessment of alternatives with grey relations (COPRAS-G) for selection of the final project. It considers environmental effects alongside traditional criteria. Innovation in this study is in the combination of the MCDMs with HOQ and prioritizing projects considering the impact on the environment. The advantages are efficiency and simplicity. The practical focus of the approach is illustrated using a case example. The approach is used for the prioritization of projects that apply the Define–Measure–Analyze–Improve–Control (DMAIC) framework in a Six Sigma organization. The evaluation of three DMAIC projects suggested taking up Project C. The illustration has shown applicability in real-life situations. Thus, the novel approach identifies an environment-friendly project that satisfies the stakeholders the most. The utilization of Grey MCDM method makes the approach suitable for use in an uncertain environment.