In this paper, an efficient global algorithm for vectorizing line drawings is presented. It first extracts a seed segment of a graphic entity from a raster image to obtain its direction and width, then tracks the pixels under the guidance of the direction so that the tracking can track through functions and is not affected by noise and degradation of image quality. Thus, an entity will be vectorized in one step without postprocessing. The relations among lines are also used to realize the continuous vectorization of a line net. The speed and quality of vectorization are greatly improved with this algorithm. The performance evaluation is carried out both by theoretical analysis and by experiments. Comparisons with other vectorization algorithms are also made.