Peter Bunyan, 53, of Brooklands Road, Cosby, pleaded guilty to manslaughter on the grounds of diminished responsibility at Derby Crown Court.
The court heard a witness saw him forcing entry into 84-year-old Brian Robson's house on 23 February.
Police then found Mr Robson with fatal head injuries. Bunyan will be sentenced at a later date.
Police told the court they arrived at the address to find Mr Robson in the hall and attempts to revive him failed.
Bunyan had returned to his house next door and was arrested there.
Det Insp Chris Barratt, from Leicestershire Police, said: "Bunyan's actions on that tragic day led to the death of a very much loved family man and devastated a family.
"I would like to offer my condolences to the family and thank them for their co-operation and understanding throughout our investigation and subsequent court proceedings."
A Leicestershire man has admitted killing his neighbour after kicking down his front door.