Objects in nature as well as man made are bound by planar as well as curvilinear surfaces. Hence the reconstruction process of three dimensional objects involves obtaining the geometrical attributes of these planar and curvilinear surfaces, lines, points etc. If a line in 3-D space is viewed from two arbitrary positions, two different images of the same line are obtained. The correspondence between this pair of projections of the line is assumed to be established in this work. The work presented in this paper describes a method of reconstruction of a line in 3-D as an intersection of two planes containing the respective projected line images. The parameters of the line in 3-D space are obtained from the parameters of projected images of the line. Relevant mathematical formulations and analytical solutions for obtaining the parameters of the reconstructed line are given. The effect of noise in the reconstruction and the efficiency of the described reconstruction methodology are studied by simulation studies.