Abstract: The hyperboloid metal walls have been widely used in the inner-external wall decorating of large buildings.The reasonable development of curved surface plays an important role in technologic simplification，material economization and quality assurance.To satisfy the requirement of tidiness of curved surface border，according to the mapping relation that keeps the distance from a dot of the flattened plane border to its center equal to the curve length from the relative dot of the curved surface border to its center，a development method of equal apothem is proposed.The engineering applications show that the method is simple and effective.