Recovering 3D geometry from a single view of an object is an important and challenging problem in computer vision. Previous methods mainly focus on one specific class of objects without large topological changes, such as cars, faces, or human bodies. In this paper, we propose a novel single view reconstruction algorithm for symmetric piecewise planar objects that are not restricted to some object classes. Symmetry is ubiquitous in manmade and natural objects and provides rich information for 3D reconstruction. Given a single view of a symmetric piecewise planar object, we first find out all the symmetric line pairs. The geometric properties of symmetric objects are used to narrow down the searching space. Then, based on the symmetric lines, a depth map is recovered through a Markov random field. Experimental results show that our algorithm can efficiently recover the 3D shapes of different objects with significant topological variations.