A discretionary lane changing model based on Stackelberg game is proposed. Lane changing is a very complex decision making process. Many factors can affect the driver to make the decision to change the lane. We only consider the discretionary lane changing case. In this case the driver want to obtain more desirable driving status through changing the lane, such as higher speed or bigger time headway, etc. Lane changing is a process of decision making. In this process the driver balances the factors and makes the decision. During changing the lane, the target vehicle and the following vehicle in the target lane can affect each other. And different drivers have different characteristics, i.e. different drivers may make different decisions under the same surrounding status. We use Stackelberg game theory to model this decision making process. Simulation is conducted to verify the proposed discretionary lane changing model.