I want to switch to the power adapter when it is connected.But my circuit doesn't work.I still get power from VBAT
The reason why that does not work is because the body diode of VT5A is still conducting even once you pull down on the SHDN pin of U7.
You will need to add a switch MOSFET to this circuit as shown in Figure 16. You only need to add the extra FET for U7. You should take a look at the LTC4418 prioritizer. That may be a better part for your application
ThanksI will use LTC4418 in a new project