After boosting the 3.3V 20khz pulse wave to 15V using a push-pull stage IGBT gate terminal input. And 24V power is IGBT's collector And I want to use the bootstrap. But it seems that the operation of this circuit is not normal. What is the problem and how can I fix it?

 

What do you expect the output to look like? What is the function of the capacitor connected to the output?

 

I saw this circuit yesterday. As I tried to point out it cannot work like this for several reasons.
The Gate of the IGBT can only get to 15 volts. (more or less) and that will not turn on the IGBT.
There is a point labeled Vge which is really Vg-gnd. It is not the voltage from Gate to Emitter.
IGBTs do turn by a voltage from Gate to Ground but by a voltage from Gate to Emitter. That is key!

This is how it is often done. Ask questions.