In this thesis, a new line detection method (FLDA: Fast Line Detection using A$\star$ algorithm) is proposed. The method uses line following method which is quantitatively analyzed in this thesis and A$\star$ algorithm which is used in graph theory to find optimum path in a graph. In order to find line using A$\star$ algorithm, the image is converted to a graph form and then A$\star$ algorithm is applied. The cost function of A$\star$ algorithm is weighted sum of gray value of candidate pixel and that of the front pixel of candidate pixel. The effectiveness of the proposed algorithm is shown by comparison with other conventional algorithms. The view points of comparison are the performance, the speed, and a priory information. As a result, its performance is very good. And the speed of the algorithm is seven times as fast as other algorithms. It takes so little operation time that it can be used for a lot of applications which have to be done fast.