Abstract: Considering about the distribution of underground fractures, the image logging information should be made the best because well drilling is very expensive. If the fracture plane is vertical to the reference plane, the project of the common line of the fracture plane and the well wall on the paper plane would be a line segment and the fracture plane position could be determined through line fitting. In the reference paper1, an algorithm was proposed, which alternately calculated the angle of the fracture plane to the reference plane and the fitted line. Yet how to get rid of the noise points near to the fracture plane is still a subject to be studied. To this end, it proposed a minimum moment theory determining the angle of the fracture plane to the reference paper plane. Further it took the advantages of line fitting and differentiates noise points from real sample points. Also it found out the difference between the direction of the linking line of two local sample points and that of the fitted line. If this difference is greater than a given small positive number, one of the end point of the linking line would be removed. Repeat this process several times to get rid of the noise points. Afterwards fit out a line with the remained sample points. Compared with previous methods, it could identify the noise points near to the fracture better.