Vedi tells the story of Prabhakaran (Vishal), a young police officer who goes to Kolkata in search of his sister Aishwarya (Poonam Kaur). Prabhakaran, at his native place, Thoothukudi, had developed enmity with a local don named Easwaramoorthy (Sayaji Shinde) by thrashing him in public and putting him behind bars. The enmity reaches Kolkata when Easwaramoorthy joins another local gangster to take revenge on Prabhakaran. The baddies trouble Aishwarya and her friend Parvathy (Sameera Reddy), who falls in love with Prabhakaran. While the enmity between Prabhakaran and Easwaramoorthy continues, a flashback of Prabhakaran goes on. Prabhakaran and Aishwarya were ill-treated by the society as their father was a smuggler. Prabhakaran decides to send Aishwarya to an orphanage, saying that he does not know who she is. This creates a bad name about Prabhakaran in Aishwarya's books. Later, Aishwarya gets adopted by a North Indian family and settles in Kolkata. In a parallel scenario, Prabhakaran locks horns with Easwaramoorthy and his pervert son Rajapandi (Amit Kumar Tiwari). They kill his mentor, who made him a police officer, and the occasion of giving a doctorate to Easwaramoorthy, Rajapandi gets tempted of a lady constable outside the stadium and rapes her inside his car. After a few years, Aishwarya's foster parents die of an accident, and she is sent to an orphanage again. Therefore, Prabhakaran goes to Kolkata and masquerades himself as Balu, a physical trainer in a college as he is scared that Aishwarya might avoid him. How Prabhakaran defeats the baddies and joins with Aishwarya is the action-packed climax of the movie.