Currently　most　of　the　analysis　about　the　running　mechanism　of　GA　focuses　on　the　convergence　problem　while　few　focus　on　population　characteristics　after　the　single　generation　descendiblity.　This　paper　presents　the　concept　of　evolution　ability　of　population　and　discusses　the　ability　of　finding　the　optimal　solution　for　the　population　after　one-generation　selection,　crossover　and　mutation.　Based　on　the　analysis　of　effect　of　crossover　on　evolution　ability　of　population,　the　experimental　results　show　that　the　important　method　for　improving　evolution　ability　of　population　is　to　include　larger　crossover　optimal　solution　area　in　a　smaller　crossover　family　area.　If　the　crossover　optimal　solution　area　isn＇t　included　in　any　crossover　family　area　of　population,　the　population　either　converges　to　the　optimal　solution,　or　evolution　will　be　trapped　in　the　premature　of　convergence.　These　conclusions　above　do　not　only　help　improve　the　GA,　but　also　provide　the　basis　for　later　research　work.　Copyright　2009　ACM.