Vedi tells the story of a young Police officer, Prabhakaran (Vishal), who goes to Kolkata in search of his sister, Aishwarya (Poonam Kaur). Prabhakaran, at his native Thoothukudi, had developed enmity with a local don (Sayaji Shinde) by thrashing him in public and putting him behind bars. The enmity gets travelled to Kolkata also where the don join another local gangster to take revenge on the police officer. The baddies trouble the police officer’s sister and her friend, Paaru (Sameera Reddy), who falls in love with Prabhakaran.
While the enmity between Prabhakaran and the local don continues, a flashback of Prabhakaran goes on. It is about how bad him and his sister were treated by the society as their father was a smuggler. So, Prabhakaran decides to send his sister to an orphanage saying that he doesn't know that girl is. This creates a bad name about Prabhakaran in his sister's books. Later, Aishwarya, Prabha's sister gets adopted by a North-Indian family and settles in Kolkata. After few years, Aishwarya's foster parents die of an accident and she is sent to an orphanage again.
Therefore, he goes to Kolkata and he masquerades himself as a Gym Teacher in a College as he is scared that his sister might avoid him.
So, how the police officer defeats the criminals and joins with his sister is the action-packed climax of the movie.