Pole-axis system is one of the main modes of Chinese regional spatial structure. It is an academic element for geographical space optimization to research urban pole-axis system spatial structure and reveal its mathematics nature. Based on pole-axis system theory, a fractal model of pole-axis system was built, and then its geographical meaning was illuminated. According to the mathematic elements of pole-axis system fractal model, this paper developed counting program of fractal model by GIS software. Taking urban-traffic system in Jinan City, Shandong Province as an example, this paper counted the parameter of its fractal model by using GIS data format. The results showed that: (1) The pole-axis system presented a fractal nature indeed when developing to a certain stage, and the fractal model of pole-axis system can effectively reflect the spatial structure of pole-axis system. (2) Fractal, scale-free and order is the different states of geo-spatial. We deduced that its spatial structure has experienced an iterative process of disorder → scale-free → fractal→ order→ a more complex disorder with the development of pole-axis system. (3) The urban-traffic system in Jinan City, Shandong Province had shaped the rudimental structure of pole-axis system, which was in the developing stage.