Neram is about the lives of Mathew (Vetri in Tamil version) and Jeena (Veni in Tamil).

Mathew/Vetri is a computer engineering graduate but lost his job. His life is a little complicated now because he has taken a loan from a private moneylender named Vatti Raja and is not able to repay the amount because he has no income. Jeena/Veni's father Johnykutty (Saravanar in Tamil) denies her marriage with Mathew/Vetri as he is jobless. Jeena/Veni decides to elope with Mathew/Vetri, and his friend John gives him money for paying off his debt to Raja. On their way, Jeena/Veni's chain is snatched, and Mathew/Vetri's money is stolen. Raja calls Mathew/Vetri and asks him to settle the money within 5PM.

Johnykutty/Saravanar lodges a complaint with Sub-Inspector Ukken Tintu (Katta Kunju in Tamil) against Mathew/Vetri on charges of kidnapping Jeena/Veni and gives his number. Tintu/Katta calls Mathew/Vetri and tells him that he should come along with Jeena/Veni to the police station within 5PM, but problems are yet to come; Mathew/Vetri's brother-in-law asks some amount of money from him to start a business (even that is scheduled for 5PM). On the other hand, Jeena/Veni is kidnapped by Raja's men, assuming her to be other man's girlfriend who also has to return money to Raja.

Mathew/Vetri comes across the same man and decides to snatch his chain, but unfortunately at the moment, he tries to snatch the chain, the man meets with an accident, and Mathew/Vetri takes him to a hospital. The man's brother RayBan (Dhandapani in Tamil), who has influence, assures Mathew/Vetri of a job in his company. Suddenly, Tintu/Katta arrives there and says that Raja died in an accident. A flashback reveals that Lighthouse, the man who stole Jeena/Veni's chain and Mathew/Vetri's money, had borrowed some money from Raja, too. He plots with two others in having the money for themselves and stealing Raja's car. While the plan works out perfectly, Raja's men went behind the car, and Raja goes behind the other man. In the chase, Raja is hit by an auto and dies. Coincidentally, the auto driver was the driver who hit RayBan's brother Manick with his vehicle, too.

Last of all, Mathew/Vetri meets the men who stole his money and involves in a brawl with them. He finds his money and a chain inside the car and also finds Jeena/Veni in the car's rear (Raja hid her in his car). Mathew/Vetri gives the money to his brother-in-law, and the movie ends with a happy note that "Time is of two types: good time and bad time. Good will come following every bad time in life".