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Since outlier detection is applicable to various fields such as the financial, telecommunications, medical, and commercial industries, its importance is radically increasing. Receiving such great attention has led to the development of many detection methods, most of which pertain to either the distance-based approach or the density-based approach. However, each approach has intrinsic weaknesses. The former hardly detects local outliers, while the latter has the low density patterns problem. To overcome these weaknesses, we proposed a new detection method that introduces the instability factor of a data point by utilizing the concept of the center of gravity. The proposed method can be flexibly used for both local and global detection of outliers by controlling its parameter. In addition, it offers the instability plot containing useful information about the number and size of clusters in data. Numerical experiments based on artificial and real datasets show the effectiveness of the proposed method.