In this paper, at first a new line symmetry based distance is proposed which calculates the amount of symmetry of a point with respect to the first principal axis of a data set. The proposed distance uses a recently developed point symmetry based distance in its computation. Kd-tree based nearest neighbor search is used to reduce the complexity of computing the closest symmetric point. Thereafter an evolutionary clustering technique is described that uses this new principal axis based line symmetry distance for assignment of points to different clusters. The proposed GA with line symmetry distance based (GALS) clustering technique is able to detect any type of clusters, irrespective of their geometrical shape and overlapping nature, as long as they possess the characteristics of line symmetry. GALS is compared with the existing well-known GAK-means clustering algorithm. Three artificially generated and three real-life data sets are used to demonstrate its superiority.