David Sinclair is accused of killing his child Joshua at his home in East Kilbride in December 2012.
Prosecutors claim the 34-year-old compressed the chest of the boy and asphyxiated him. It is also alleged Mr Sinclair seized hold of the child and shook him repeatedly.
The indictment claims he inflicted "blunt force trauma" to Joshua by means unknown.
The child is said to have been left so severely injured he died at Hairmyres Hospital in the South Lanarkshire town.
Mr Sinclair faces a separate charge of attempting to murder his baby son.
The accusations span from a day after Joshua was born to the day before he is said to have been killed.
Mr Sinclair made his first public appearance in the dock during a hearing at the High Court in Glasgow on Friday.
Ian Duguid QC, who was representing Mr Sinclair, entered not guilty pleas on his client's behalf.
Judge Lady Scott set a trial due to start in July with the case expected to last four weeks.
A man is to stand trial charged with murdering his five-month-old baby son.