In 3D edge detection for an industrial Computed Tomography(CT) image, the Facet model can be used to obtain the relatively precise image edge, but it will cost too much time. Otherwise, the wavelet transform method can be taken to detect 3D image edges in a shorter time, however, the edge information obtained depends on the threshold strongly . In combination with the characteristics of two methods above, a 3D edge detection method based on wavelet transform and Facet model is presented in this paper. Firstly, 3D wavelet transform is used for an industrial CT 3D image , and initial candidates of edge could be obtained by setting a smaller threshold. Through this step, the edge is located roughly. Then, 3D Facet model is used to decide if the candidate is the true edge, and the points in rough edge are fitted one by one to realize the precise location of the image edge. The improved algorithm reduce the number of edge pixel candidates by the preprocessing of 3D wavelet transform, which improves the detection speed of the original 3D Facet model. Experimental results show that the proposed method not only can obtain the same image edge as that by original 3D Facet model but also can improve the image detection speed greatly. Obtained results indicate that the image detection speed has increased by 3.51-7.39 times as compared with that of original 3D Facet model, and the simpler the image edge is, the higher the accelerate ratio is. These results show that the 3D edge detection method based on wavelet transform and Facet model can meet the requirements of the 3D image in an actual industrial CT for high accuracy and high speed.