Social workers had received warnings about Marcus Bebbington and placed his four-month-old son, Kristian, on the "at risk" register. Last July, Bebbington, from Norwich, broke the boy's skull in two places, after consuming five cans of lager and a pint of vodka.
At Norwich Crown Court David Stokes, for the prosecution, said in the past 16 years Bebbington, 34, had been given custodial sentences totalling more than 10 years. Bebbington denied killing his son, saying he was too drunk to recall what had happened.
Sentence was adjourned.