The position and pose reconstruction of spatial hole widely exists in industrial and architecture areas. This paper proposes a method for recognizing the position and pose of space hole, named the directrixgeneratrix method. The principle of the reconstruction method is as follows: fitting the hole directrix according to the marginal points on the cross section of the hole; through other points in hole cylindrical surface respectively, drawing the hole cylindrical surface generatrix in the direction given by the hole axis; LM (Levenberg Marquard) algorithm is adopted to perform the optimization, in which the algebraic sum of the distances from the crossover points of the generatrices and the hole cross section to the hole directrix is minimum. Then, the hole axis direction is obtained, and the center of hole directrix could be used as the hole location. The experiment result shows that the proposed method requires less sample data, and features very simple calculation process and high accuracy, which is also suitable to the position and pose reconstruction for axis and other cylindrical surfaces.