I'm not sure this fits exactly, and I also saw you already dropped it after an episode, but Que Sera Sera could work, too. Kang Tae Joo isn't a criminal, but he is a pretty despicable character, and not just in the typical cold and arrogant drama hero way: he's a "gigolo" of sorts, because he dates rich women for money. Of course, opposites attracts and he falls for a quirky poor girl (set up sounds cliché, but the characters are incredibly complex and alive). I'd say up until the last episode, his decisions are reprehensible, but that doesn't make him unrelatable for the viewer either. He really, really does fall in love, only his greediness is so strong he doesn't know how to deal with these unknown feelings, and ends up hurting everybody around him because of it, himself in particular. It's a very unusual drama in my opinion -- on paper it may seem melodramatic, but it's actually quite realistic and stark (without being depressing either, which is why I like it. I understand why it's not everybody's cup of tea though!
Then I'll mention these two chinese dramas, but I'm not sure I would exactly recommend them because personally, I think they're both rather bad quality (I'm loosely following them in a junk food kind of way :p): Cruel Romance and Lady & Liar. Both male leads are gang leaders and are pretty mean, although they're presented as heroes from the female leads perspective (constantly saving her blablabla -- unlike Que Sera Sera, in which the male lead is quite the anti-hero, and yet felt so much more human and touching!).
Good luck!