Recently, identification of modal parameters using the response only data has attracted considerable attention particularly where the classic modal testing methods is difficult to conduct. One drawback of the response only data, also known as Operational Modal Analysis (OMA), is that only the unscaled mode shapes can be obtained which restricts the applications of OMA. The Mass change method is a usual way to scale the operational mode shapes. In this article a new method is proposed to optimize the additive mass for scaling of the unscaled mode shapes from OMA for which a priori knowledge of the Finite Element model of structure is required. It is shown that the total error of the scaled mode shapes is minimized using the proposed method. The method is validated using a numerical case study of a beam. Moreover, the experimental results of a clamped-clamped beam demonstrate the applicability of the method.