Abstract: Starting from the Bird′s Nest, the main venue of the 2008 Beijing Olympic Games, several twisted, skewed, and twisted grid-shaped buildings have appeared in China. Among them the most representative are the North Bird′s Nest Nanchun Cocoon and the Beijing Phoenix International Center. The twisted and skewed grid structure is favored by architects for its beautiful and unique shape. In this paper, the geometric theory is combined with actual engineering, and two geometric methods for parametric design of bending-torsion-skew grid structure are proposed. First, the geometric geometry of the curved and twisted grid structure is analyzed by differential geometry methods, and the analytical expression of the surface parametric equation is given. Second, from the perspective of kinematics, through the geometrical methods such as movable frame, sweeping and lofting, and using computer-aided graphics methods to obtain the geometric model of the twisted and skewed grid structure. The effectiveness of the two methods has been verified in the engineering practice of the table tennis hall of Hangzhou Asian games.