Decision-making　model　of　speeding　and　no　speeding　of　drivers　and　inspection　and　no　inspection　of　traffic　mangers　is　proposed　aiming　at　the　speeding　behavior　of　drivers.　The　evolutionary　process　that　traffic　mangers　and　drivers　choose　strategies　is　analyzed　using　evolutionary　game.　The　possible　evolutionary　stable　states　are　analyzed　accordingly　to　local　stability　of　Jacobian　matrix.　The　evolutionary　stable　state　has　several　kind　conditions　such　as　saddle　point,　stability　point　and　instability　point　because　of　traffic　mangers　and　drivers＇　different　benefit.　The　results　show　that　government　department　must　reward　traffic　mangers　for　doing　their　duty　and　punish　traffic　mangers　for　their　breach　of　duty　to　urge　traffic　mangers　to　inspect　strictly.　At　the　same　time,　the　speeding　drivers　should　be　punished　strictly　according　to　individual　difference.　Thus　speeding　driving　can　be　forbidden　to　a　certain　extent　and　improve　traffic　safety.　©　2010　by　Science　Press.