The invention describes a method for converting graph elements containing sparse graphs into a graphic layer, comprising the following steps: correspondingly mapping each sparse graph to each sparse graphic layer, and projecting conventional graphs between the sparse graphs in turn according to the bottom to top sequence on a projection plane to form a conventional graph combination layer. The invention also describes a method for displaying in a rapid and flicker-free way by using reduplicated sparse graphs of arbitrary shapes, comprising that: converting the graph elements containing the sparse graphs to be displayed into the graphic layer, judging whether the sparse graphs to be displayed are needed to be drawn or erased, setting each point on the corresponding sparse graph as transparent when erasing the sparse graphs, and completing the drawing of the corresponding points of the shape of the sparse graphs according to the shape of the sparse graphs to be displayed. Moreover, the invention also describes the corresponding device of the above mentioned method.