Naresh Kumar, 25, was killed by his father Sita Ram around 12.15 a.m. Monday in north Delhi's Shalimar Bagh.
Kumar, a habitual drinker, had demanded money from his mother to buy liquor.
"When she refused to give him money, he started beating her. He also got into a fight with his father, who then hit him on the head with an axe that led to his death," said a police official.
Police said that they have arrested Sita Ram.
Kumar used to regularly beat his parents whenever they refused to give him money to buy liquor, police said.