The 19-year-old youth, a student of standard 12, was speaking through the window with the girl, who was inside her home last night. Her father suddenly appeared at the spot and fired at him with his gun.
As the youth fell on the ground the locals rushed to the spot and rushed him to hospital, where the youth was declared brought dead.
The man was arrested later in the night, the police said.
Nadia superintendent of police Bhaskar Mukherjee confirming the incident said the man was allegedly against his daughter's relationship with the boy.