
Kaohsiung City, the heart of southern Taiwan, is 300 kilometers away from Taoyuan International Airport. Thus, taking a bus or driving are not recommended to visitors. The most recommended and time-saving way to go to Kaohsiung directly from the airport is taking THSR.
By THSR

Passengers need to take Taoyuan MRT first and then transfer to THSR at A18 Taoyuan HSR Station.
Taoyuan Airport MRT | TSHR | Total | |
Duration | 20 mins | 95 mins | 115 mins |
Fee | NT$25 | NT$1330 | NT$1355 |
By Taiwan Railways

Just like taking THSR, travelers have to take the bus to the Taiwan Railway Taoyuan Station first.
Bus Route 706 | Bus Route 5059 | |
Duration | 40-60mins | 40 mins |
Fee | NT$48 | NT$53 |
The fare for Tze-Chiang Limited Express and Puyuma from Taoyuan to Kaohsiung is NT$777. You can check the timetable and book the train ticket here.
How about Freeway Shuttle Bus service
You can still take the freeway bus to Kaohsiung. However, there’s no bus headed to Kaohsiung from the airport. You might have to go to Taipei and then transfer to Freeway Shuttle Bus service. As for how to go to Taipei from the airport, please refer to this article.

Once you arrive at Taipei Main Station, it’s easy to find the Taipei Bus Station. Just follow the direction signs and go through the underpass. There are several companies provide transportation service so the ticket price is cheap. The fare for a single journey ticket to Kaohsiung is NT$590.