Abstract: It is usual to plot three-dimensional graphics formed by two or more surfaces by Mathematical software such as MATLAB, MAPLE. The principle of the computer drawing is to plot the sample points, then draw lines through these points to form a diagram. Sometimes, because the data points are too many, the domains available for dot-gathering are limited, the graphics overlay tends to cause the problem of the diagram drawn failing to reflect the realistic shape of intersections. In order to quickly plot three-dimensional graphics formed by two or more surfaces, hand drawing is sometimes necessary. The difficulty of this hand drawing is to draw the intersection of any two surfaces. Firstly, simplify simultaneous equations, and then in combination with projection and parallel cutting method sketch the accurate intersecting curves. The mathematical principle and general steps are given for the sketch method. From students’ works by this method show that the sketch method is of strong operability and is easy to grasp