Line drawing images are the most proper information to represent the characteristics and shapes of digital images and used for recognition and communication. For the coding of line drawing images, common eight-direction chain code is used mostly. In the paper, the new mode selection chain code method is proposed which can compress the eight-direction chain code about twenty percents and be used for the reversible coding method of line drawing images. In this coding techniques, we set a reference mode for each quadrant around an abject pixel, and assign 3-directional code for these reference modes. Therefore a line pixel is coded with 3 bits. Also, a new corner finding method of line drawing images using this mode selection chain code is proposed in this paper.