For different time variant target functions, control laws of closed quantum systems are designed by means of the Lyapunov stability theorem. The problems of excessive control fields during the period of tracking are solved through the use of the adaptive algorithm. System simulation experiments are implemented for different target functions. Under the action of control law, the control system can track from its arbitrary initial state to the target system. The experimental results show that the control strategy proposed has the ability to adjust the control law adaptively and real-time track dynamic target systems during the  eriod of tracking, and that the control strategy proposed has common characteristics for different target functions.