This paper presents a progressive algorithm that not only can narrow down the search domain in the course of face identification but also can fast reconstruct various 3D objects from a sketch drawing. The sketch drawing, edge-vertex graph without hidden line removal, which serves as input for reconstruction process, is obtained from an inaccurate freehand sketch of a 3D wireframe object. The algorithm is executed in two stages. In the face identification stage, we generate and classify potential faces into implausible, basis, and minimal faces by using geometrical and topological constraints to reduce search space. The proposed algorithm searches the space of minimal faces only to identify actual faces of an object fast. In the object reconstruction stage, we progressively calculate a 3D structure by optimizing the coordinates of vertices of an object according to the sketch order of faces. The progressive method reconstructs the most plausible 3D object quickly by applying 3D constraints that are derived from the relationship between the object and the sketch drawing in the optimization process. Furthermore, it allows the designer to change viewpoint during sketching. The progressive reconstruction algorithm is discussed, and examples from a working implementation are given.