In the case of complete information, it is of great significance that use cubic Bezier curves which used as primitive form standard in graphic system to express the spatial data for data processing and transmission. In the text fonts of map, it is customary to use straight lines and the set of quadratic Bezier curves to describe the glyph outlines,but it is inconvenient in the process because the quadratic Bezier curves are non-standard curves. Based on this situation, in this paper,it is proposed the method of quadratic curves fitting using cubic Bezier curves and derive corresponding computing formula. The method is that remove the characters glyph outlines which are described by curve edges from the font and fit the curve edges with quadratic Bezier curves, finally the curve edges are fitted by cubic Bezier curves segment by segment. Through the result of the experiment, it proves that the differences between fitted cubic Bezier curves and quadratic Bezier curves to be fitted are small. The text graphics curves expressed by the method represent the geographical features effectively and provide an effective way of the transformation from font text to the map text.