Thomas Black, 62, of Gretna, admitted driving carelessly and colliding with a stationary car driven by the baby's mother causing it to spin into the path of an oncoming vehicle on the A75 near Carrutherstown, Dumfriesshire.
Both cars then left the roadway and baby Oliver Hewson was severely injured and died. His mother Suzanne and the driver of the other car, Rebecca Thompson, were both injured.
Black pled guilty at Dumfries Sheriff Court to driving at excessive and inappropriate speeds for the prevailing road layout, failing to keep a proper lookout and failing to notice Mrs Hewson's car stationary at the road junction.
He admitted failing to brake or take evasive action in time to avoid colliding with it.
Sheriff George Jamieson told Black: "The court will be considering a sentence of imprisonment and as you have not received any prison sentence previously I will have to obtain reports and you will be banned from driving meantime."