The man had returned from Kerala, where he worked, to his home at Abhoypur in West Bengal's Nadia district on Friday last after two-and-half years.
Finding the one-and-half year old baby boy at home and told by locals that his wife was in a relationship with another person, he suspected his wife's fidelity and strangulated the two to death on Saturday night, the police said.
He also injured one of his minor daughters aged three years with a sharp weapon, the police said.