The utility model relates to a system for drawing a curved surface by calculating all real roots and multiple numbers of a zero-dimensional trigonometric polynomial system. The system comprises an implicit expression curved surface equation generating device, a curved surface feature point generating device, a curved surface connection relationship diagram generating device, a curved surface drawing device and a display device, wherein the curved surface feature point generating device acquires the feature points and multiple numbers of the curved surface by calculating all real roots and multiple numbers of the zero-dimensional trigonometric polynomial system; the curved surface connection relationship diagram generating device acquires a connection relationship diagram through determining the connection relationship among the feature points; the curved surface drawing device draws a mesh curved surface on the basis of the connection relationship diagram directly or draw the smoother curved surface through other light naturalizing methods; and the display device displays the obtained curved surface image.