For getting the parametric equation of random polygon, by the basic extension factor to stretch the round, there generates polygon of meeting the required conditions. Such algorithm overcomes the disadvantage in the generation of polygon from round under control of a single parameter and the complication of mathematical background. Firstly, a detailed introduction is given to the basic extension factor and the selection of relevant coefficient, and then the errors of such algorithm are analyzed. And the experimental result shows that the mathematical background of such method is relatively easy, the parameters are easy to control and constitute, and the generation of arbitrary polygon is available with high precision. Such the parametric equation of random polygon and method can be used in relevant fields such as geometric modeling, CAD/CAM, and computer graphics.