Edge enhancement in potential-field data helps geologic interpretation, where the lineaments on the potential-field frequently indicate subsurface faults, contacts, and other tectonic features. Therefore, a variety of edge-enhancement methods have been proposed for locating edges, most of which are based on the horizontal or vertical derivatives of the field. However, these methods have several limitations, including thick detected boundaries, blurred response to low-amplitude anomalies, and sensitivity to noise. We have developed the spectral-moment method for detecting edges in potential-field anomalies based on the second spectral moment and its statistically invariable quantities. We evaluated the spectral-moment method using synthetic gravity data, EGM-2008 gravity data, and the total magnetic field reduced to the pole. Compared with other edge-enhancing filters, such as the total horizontal derivative (TDX), profile curvature, curvature of the total horizontal gradient amplitude, enhancement of the TDX using the tilt angle, theta map, and normalized standard deviation, this spectral-moment method was more effective in balancing the edges of different-amplitude anomalies, and the detected lineaments were sharper and more continuous. In addition, the method was also less sensitive to noise than were the other filters. Compared with geologic maps, the edges extracted by the spectral-moment method from gravity and the magnetic data corresponded well with the geologic structures.