I can not say that I'm 100% sure but I think I was dating Kim Ha-neul, that what I heard in other Forum. I don't know if there a still togehter.

I thought he was with Choi Ji Woo but can not confirm they just be rumored to be together.

I think that he is single now. I wish he would
be with Choi Ji Woo. They would be cuteeest
couple ever.

I love to see him and Kim Ha-neul as a couple.I only know that he want to marry. I found an interview:

Actor Kwon Sang-woo revealed that he would like to marry before becoming 35.

He said in an interview with Sports Korea, "If there was someone I was seeing, I would like to marry even now. I think I need to marry before I become 35 in order to have children and raise a normal family. I don't want to go beyond 35".

It is time for Kwon Sang-woo to be thinking seriously about marriage, for he turned 33 this year. He must also think of his parents, who are expecting him to marry, for his older brother of five years married already. He said, "If you're not an actor, you should be married by this age".

After debuting in 2001 in his twenties, he is now moving towards his mid-thirties. He joked, "I was so fresh before. If I look at how I looked at my debut, I feel I got a lot older. It's hard for Asian actors to stay handsome even with age. I want to remain handsome".

He received the role of a violent gang member in the movie "Fate", coming out on the 20th. It is his first evil char.

I have seen interview clips of him and Kim Ha Neul. They were soooooooooo adorable together. He seemed to adore her, how he would look at her adoringly, tease her and tell numerous funny stories about her from the set. He knew so many stories and with so many fine-tuned details, and he would be so delighted while telling these stories, often jumping up from his seat to act them out–it was easy to see they had something going. If it ended that’s really too bad. Cute couple.

I just found a video that shows that Kwon Song Woo is sitting behind of Kim Ha Neul. Instead of sitting next to her!
watch this: link

It shows clearly that they never were not together . He actually totally ignored her.

Recently, I heard from others he was ones together wit Soh Yoo Jin, who is actress. She now plays for tv series "Thirty Thousand Miles in Search of My Son". They were 3 1/2 years together.