An important research area in computer vision is developing algorithms that can reconstruct the 3D surface of an object represented by a single 2D line drawing. Previous work on 3D reconstruction from single 2D line drawings focuses on objects with planar faces. In this paper, we propose a novel approach to the reconstruction of solid objects that have not only planar but also curved faces. Our approach consists of four steps: (1) identifying the curved faces and planar faces in a line drawing, (2) transforming the line drawing into one with straight edges only, (3) reconstructing the 3D wireframe of the curved object from the transformed line drawing and the original line drawing, and (4) generating the curved faces with Bezier patches and triangular meshes. With a number of experimental results, we demonstrate the ability of our approach to perform curved object reconstruction successfully.