Ok, finally I found the song. it was "Aldrig Skall Jag Sluta Älska Dig", from the movie "Livet Är En Schlager" written by Jonas Gardell.
When I was watching Jonas Gardell's performance on Melodifestivalen, I just felt that this song was so familiar to me, but I couldn't recall where I had heard this song before. Now I remember that it was from that movie I watched 2 years ago in Sweden - though I don't speak Swedish, the movie not difficult to understand and I think it's pretty good.
Jonas performed it in a quite dramatic way though, it's very touching. Now I can only find the soundtrack version of that song, sung by Helena Bergström.
By the way, when I was searching for this song, I just realized that Jonas is gay, and together with the other host that night, Mark Levengood, they are probably the most famous gay couple in Sweden! Well, nobody told me about it before, and obviously I don't have a gaydar installed :-)