Nami Island is now accessible by subway. This is because recently, a new track had been built. Since it was a new track, not all subway maps were updated with it.

To get Nami Island by rail:

One need to go to 회기 (Hoegi) located in Line 1. The station is shown on the old map so no worries. From there, transfer to another line that goes to 중랑 (Jungnang). However, do not get off from here but only at 상봉 (Sangbong Station). From here again, take another track that goes to 춘천 (Chuncheon) in Track no. 5 as the last station. GET OFF at 가평 (Gapyeong)

회기 (Line 1 and 중양) -- 사봉 (중양 line) -- 가평 (At new line)

From the exit of the station, take a taxi to Nami Island. Just tell the driver "남이섬 (Nah-Mee-Som or Nami Island)" and the journey will cost less than 4000 Won.

The above were taken frm other ppl blog and i personally experienced the new route all by subway until to gapyeong. It was easy, dont worry.

I dont think that one is the new subway line. The new extension still take you to Gapyeong and you still need to take taxi to Nami island.

When u r in line 1 or line 4, u can stop at Hoegi, Line 1 and take the new subway extension that connected to Sangbong, Line 7. You cannot see this in Seoul Subway map because most of the map is not updated. Then from Sangbong take the new extension subway to Gapyeong.

Initially I also tot of taking express bus from insadong but "luckily" all tickets were sold out then mai ask the lady in the counter is there any other way to nami island lor. Actually is the lady that told us we can go to nami by subway. Then only i searched up and down in the internet to confirm her saying and manage to search a blog that mentioned the same thing.