A method based on linear singularity analysis of image is presented. The improved method, called Directional Beamlet Transform (DBT) is better than traditional Beamlet transform about directional information of image and has the ability of representing linear-singularity of image. According to the analysis of linear singularity, edge detection is transferred to detecting singularity point in the coefficient matrix of DBT. Because the noise has point-singularity and the edges have linear-singularity in noisy images, the method based on linear singularity analysis can reduce the influence of noises. The experimental results on manual images and SAR images demonstrate the effectiveness of this method. Compared with traditional edge detectors, it is shown that proposed method has the ability of anti-noise and linear connection.