To characterize reservoirs with complex fault blocks or lithology, geophysicists often need to depict the edge of geologic bodies such as small faults. Edge detection is a powerful tool for structural feature identification; however, conventional edge-detection operators that are widely used in image edge detection are not always adequate for seismic data. In fact, most conventional edge-detection methods are effective along a plane. For seismic data, it is more appropriate to detect edge information along the slope of an event. We evaluated a new method for fault detection based on a surface-fitting algorithm. The surface-fitting algorithm was used to find the local slope of a seismic event, and then edge detection is performed along this local fitted plane. For each point in a seismic volume, we defined a small neighborhood in a plane parallel to the local reflector with the help of dip estimation. The data in the neighborhood were then approximated by a bivariate cubic function, called the facet model. Then, the local gradient of the function is calculated and referred to as the facet model attribute. To enhance the robustness of the output attribute and suppress noise, the gradient values were summed over a vertical window and normalized by the energy. To evaluate the performance of our method, we also calculated the dip-guided Sobel attribute and variance attribute. Compared with these three attributes, the result of our method suggested more accurate edge detection, and it showed more detail in fault detection.