Taipei to Green Island is doable in a single day. The smoothest route is an EMU3000 Tze-Chiang Limited Express or Puyuma Express to Taitung, then Puyuma Transport Route 201 from Bay 1 outside Taitung Train Station to Fugang Ferry Pier (Taitung), then a ferry jointly operated by Kaixuan, Tianwangxing and Lyudao Star to Nanliao Harbor (Green Island).
Taipei to Taitung takes about 3.5 hours at the fastest (Puyuma / EMU3000), Taitung Train Station to Fugang is roughly 20 minutes for NT$25, and the Fugang to Nanliao crossing runs about 50 minutes. Add boarding time and walking, and plan on 5–6 hours door-to-door to be safe.
The Green Island route runs 2 fixed sailings on weekdays (outbound 09:30 and 13:30; return 10:30 and 14:30). In high season and on weekends and holidays it scales up to 5 sailings a day (07:30 / 09:30 / 11:30 / 13:30 / 15:30) depending on bookings. The cleanest combination: leave Taipei a little after 06:00 on an EMU3000 Tze-Chiang or Puyuma Express, arrive Taitung around 10:00, then catch the 11:30 Route 201 to connect with the 13:30 sailing.
If you want the high-season 07:30 extra sailing, take the late-night EMU3000 red-eye from Shulin (departing around 23:00), arrive Taitung around 05:00, board the first Route 201 at 06:20, reach Fugang at 06:40 and wait 50 minutes for the boat.
The last sailing of the day is the high-season 15:30 extra; on weekdays the last one is 13:30. Miss it and you'll need to overnight in Taitung — plenty of stays around Taitung Train Station — and try again the next morning. Use ferry.tw for tickets and same-day capacity; sailings can be cancelled at short notice for typhoons or a strong northeast monsoon. The tables below show live TRA, bus and ferry times for the date you load this page.