Hi, May I know is there any typhoon in Taipei / taiwan on 18 June - 21 June? Thanks

Usually, there is little chance that typhoon happens in June, for high-incidence season is often in August and September. So don't worry, just keep close attention to the weather report before your departure.

Thanks Helen. May I know which website is accurate to check the weather? and how to know the weather shown is typhoon?

Well, you can check the weather of this area in this website.
The relevant weather statistics are update and reliable. You can take this website as a reference.
In addition, the sign of typhoon is just like a whirlwind. Generally speaking, June to October is the typhoon season of this area.