The method to polygon' intersection is applied in computational geometry, computer graphics, GIS, evaluation of geo-hazards and civil engineering. Based on the node state of polygon, the authors propose the method and algorithm of polygon' intersection, the key to which is node operation. This method's concept is simple; and it is easy to computer program's implementation. It avoids to singular problem of Boolean Operation, and is easy to solve the problem of overlapping side and sides intersecting in node of polygon. For the arbitrary way of intersecting of arbitrary solid polygon, this method is accurate and general.