Mohamad Ali, 19, after an argument with his step mother at Kunduli village allegedly hacked her to death with a sharp weapon, police said.
He then attacked her minor daughter and son killing them on the spot, they said.
The neighbours claimed that Mohamad and his step mother would often fight after his father married her and shifted to another house following the death of his mother.
The deceased have been identified as Phulbano Khatun, Nazia Khatun and Rabiul Hussain.
Mohamad Ali is missing, they said, adding a search has been launched to trace him.