Criminal Drama Suggestions

Hi I've recently been wondering if there is any Asian Dramas about a criminal who falls in love with the main girl. I haven't seen this kind of concept before and I would be really thankful if someone suggested any dramas they know that are like that.

I have seen cruel city... it more or less fits your requirement of a criminally-labelled character in love with a main female, but the romance hits a certain point where it sees no more development because it's not a focus for the drama or for jung shi hyun's character to pursue it.

maybe love me if you dare? I started this & I only know so much about it, but it didn't feel like something I could get into. 

I don't think it's what you have in mind, but there's also boku no yabai tsuma. very gone girl within the first two eps, but it branches into its own story after that. 

I can think of a few more dramas, but they don't necessarily involve a criminal falling in love with the female lead & are more along the lines of obsession, or the female isn't a main, etc.

you might like kdrama Triangle, male lead is not a killer, but he's thug life (with a kind heart) been through jail and is really at the lowest of society, he is often getting into trouble and involved with the wrong kind of people. Female lead is a humble girl who is also in the poor pool and doing her best to get by. But they have an endearing connection and strong chemistry throughout.

Also in ep 1 of http://mydramalist.com/18716-the-gentlemen-of-wolgyesu-tailor-shop
at 25:33 there is a scene of Gangster who has been in love with female lead since they were youth. While he's not the main male lead, his moments and their flash back scene is sweet.

Shark
Two Weeks
City Hunter
That Winter, The Wind Blows ( I don't like this drama but lot of people love it...and it falls into your category so check it out and see if you can :)

Legend of the blue sea (kind of fits)
Kaitou tantei yamaneko
Maou