How to take public transport from Taoyuan Airport to Ximen Station using local public transport ?

Do you refer to the Ximen Metro Station in Taipei? You can take bus no.1819 to Taipei Railway Station first. This bus works for 24 hours with the duration of 55 minutes or so. The ticket fare is CNY125/person. Upon arrival, you may walk about 500 meters to Taipei Metro Station and take line 5 to Ximen Station directly.