I want to watch a drama where ML is a grey character. He has some sort of motive like revenge to approach FL but can’t help fall in love with her. FL doesn’t fall for his tricks. She can see that he has some ulterior motive and doesn’t fall for him. He becomes possessive about her while falling for her. But she takes time to fall in love with him.

These are along those lines but not exactly (sort of the general concept of ML approaches FL with ulterior motives, and in some of them he's a bad guy).

  • My Lady General (ML is an assassin who takes another guy's identity and marries the FL in order to get a cure for his poison that she has. He falls for real, she finds out who he is and wants nothing to do with him. He manages to win her heart, though.)
  • Untouchable Lovers (very grey ML who approaches FL with the intention of sacrificing her to change his fate. FL is quite reluctant to trust him at times and constantly suspects he's plotting something.)
  • Well-Intended Love (ML manipulates and creates a false story of the FL having cancer and needing his help in order to make her marry him because he's been obsessed with her for years. Needless to say, she's not pleased when she finds out, but the two do end up happy together in the end.)
  • Moonlight Romance (FL has magical "butterflies" that the ML needs to survive and return home, the FL finds out about why he approached her and pushes him away until she realizes he really ended up loving her.)
  • Back From the Brink (ML is initially using the FL to get back his scattered body. FL falls first in this one, but he ends up stabbing her and there's an arc where she is terrified of him, and he realizes what he's done and that he loves her and tries to win her back.)
  • The Journey of Flower (FL is prophesied to turn evil, ML approaches her under the guise of being her teacher in order to keep an eye on her and kill her if she turns evil.)
  • The Miraculous Girl (ML "buys" FL to use her magical blood as a cure for his terminal illness. She's actually using him too. )
  • The Princess and the Werewolf (ML marries the FL to get back an object of his she has.)
  • Yes, the False Judge (bandit ML pretends to be the judge fiancée of the FL to accomplish a goal.)
  • Your Sensibility My Destiny (ML abducts the FL and keeps her in his mansion because she can magically give him his missing senses/emotions.)
  • Angel's Last Mission: Love (ML approaches FL as his mission to help her find love in order to allow him to return to heaven. He ends up falling in love with her himself, and even sacrifices himself to save her. There's a happy ending, though.)
  • Bossam: Steal the Fate (ML does a lot of shady jobs and one of those is abducting women for other guys to marry. He accidentally abducts the FL, initially tries to kill her when he realizes her family destroyed his, can't go through with it, and later falls in love with her.)
  • Bulgasal: Immortal Souls (ML hunts down the FL to kill her in revenge, ends up falling in love.)
  • City Hunter (ML approaches FL as part of his revenge plot, ends up falling in love and rethinking everything.)
  • Doom at Your Service (ML uses FL's wish to his advantage, FL hates him at first.)
  • Healer (ML approaches FL under a false identity as a job he's hired to do.)
  • Ferryman: Manjusaka (movie, ML approaches FL acting innocent and pretending to fall in love with her in order to get something she has that his sect needs. He ends up falling in love for real and goes against his sect.)
  • Hanaoni (movie, ML is a demon who chooses and allows the FL to be on her own hunted by demons in the hopes that she'll die and he'll be freed from the position he's born into and hates. She survives, shows him kindness, and he ends up falling in love.) 
  • Love Better Than Immortality (very grey ML who approaches the FL but with genuine interest, not a motive. FL is very cautious at first.)

Behind Your Smile - the ML is sheltering the FL in the hope of luring her mother, a businesswoman who seemingly swindled hundreds of people and disappeared. He is bitter and blames the mother for the death of his father. The problem is that she is just so nice, like having a puppy around.

Thank you for the reply emeraldarrows.