I can think of a couple that might be right up your alley:
Goong - The guy in this drama is kind of a jerk, though. It really took me a long time to see what the girl saw in him that made her hold on to him so much. Pursue might be a strong word for how she tried to hold onto him, but it's close enough I suppose :p
Playful Kiss - I didn't like this drama, Ha Ni was a ridiculously weak female character, and I just wanted to tell her to move on already. But she definitely is in hot pursuit of Baek Seung Jo the entire drama. It just depends on if you don't mind your females weak and insipid.
Personal Taste - Again, pursuing is a strong word for the relationship, but the girl in this drama at least recognizes her feelings and admits to them first in this drama. She is just hampered by the whole thinking Lee Min Ho is gay aspect :p
But I would like to second the My Girlfriend is a Gumiho recommendation it fits what you are looking for perfectly. Shin Min Ah plays a Gumiho who is set free by Lee Seung Gi's character and from the get go, she decides she wants to be around him and makes his life just a tad miserable in the beginning. It is hilarious and does have some really good romance in it. Easily one of my top 10 dramas :)
I would also like to throw
Love Rain out there as a suggestion. It has Jang Geun Suk from You're Beautiful in it, and it is a really good drama. It starts with JGS pursuing Yoona's character, but the tables get turned and she ends up going after him.