Reconstruction of a line in 3-D space using arbitrary perspective views involves the problem of obtaining the set of parameters representing the line. This is widely used for many applications of 3-D object recognition and machine inspection. A performance analysis of the reconstruction process in the presence of noise in the image planes is necessary in certain applications which require a large degree of accuracy. In this paper, a methodology, which is based on the concept of epipolar line, for the reconstruction of a 3-D line, from two arbitrary perspective views is given. In this problem the points in the second image plane, which correspond to points in the first image plane are found by using epipolar line method, by considering all the points in the first image plane. Then triangulation law is used to find the points in 3-D space. Using least square regression in 3-D, the parameters of a line in 3-D space are found. This least square regression problem is solved by two different methods. Simulation study results of this epipolar line based method, in presence of noise, as well as results of error analysis are given.