Two weeks also called 2 weeks is about a man named Tae-San (Lee Joon-Gi) lives his life meaninglessly. He is falsely accused of murder. The man learns that he has a young daughter stricken with leukemia.
For the next two weeks, he struggles to save his daughter. 8 years ago, Tae-San and In-Hye (Park Ha-Sun) were involved in a romantic relationship. At the time, Tae-San was a member of a crime gang and worked for crime boss Moon Il-Seok (Jo Min-Gi). One day, Moon Il-Seok ordered Tae-San to take the wrap for a murder charge that Moon Il-Seok committed.
If Tae-San refuses, Moon Il-Seok threatens to kill his girlfriend In-Hye, who is pregnant at the time. Tae-San agrees to take the fall and goes to prison, but first he takes In-Hye to an abortion clinic. In-Hye has no idea why Tae-San changed. Now, Tae-San is still a gang member and works under Moon Il-Seok, but he’s looked down upon by the other guys. Tae-San also works at a pawn shop run by his gang.
One day, Tae-San is about to hit another guy there, but stops when he sees a woman through the window. The woman is his ex-girlfriend In-Hye. They sit together in a coffee shop. In-Hye then asks Tae-San to take a blood test. Tae-Sun is confused by her request, but learns that she has an 8-year-old daughter named Soo-Jin (Lee Chae-Mi). Her daughter also has leukemia and desperately needs a bone-marrow transplant. Tae-San also realizes that when he took In-Hye to the abortion clinic 8 years ago, she did not go through with the abortion and that Soo-Jin is his daughter.
In-Hye lets Tae-San know that she has no interest in restarting a relationship with him and that her fiancé Seung-Woo (Ryu Soo-Young) is a detective. After going to the hospital for the blood test, Tae-San learns that his bone-marrow is a match and he can go ahead with the transplant operation in 2 weeks. But, Tae-San goes to see someone and when he wakes up he is arrested by two detectives for her murder.