This paper deals with on-line signature verification. A signature is obtained as a sequence of x, y-coordinates of pen-tip movement and writing pressure. The features of a signature are derived from the coordinates and the writing pressure and are decomposed into two principal features, shape and motion, using the DP-matching technique. We found that each point of a signature varies each time to some degree. However, the degrees of local variations subject to points, as some points are relatively stable and do not vary much while some of them are not. In this paper, we propose to incorporate weighted local variations based on the stability of each point so as to evaluate the difference of two signatures locally as well as globally. The dissimilarity measures are presented with respect to the corresponding features and are combined into one for efficient verification. In addition to the x, y-coordinates, the writing pressure is also considered to be part of shape. Experiments were carried out with a database which consists of 300 genuine signatures and 300 forgeries collected from 10 subjects. The effectiveness of incorporating the weighted local variation is shown by the experimental results. It contributes to an average increase in the correct verification rate as the correct verification rate increased 1.0% and was found to be 98.7%.