Andrew Rose was remanded in custody when he appeared before Birmingham magistrates on Wednesday.
The 33-year-old is charged with causing serious injury by dangerous driving, grievous bodily harm and driving without a licence or insurance.
The charges relate to a collision on the A34 Walsall Road, Great Barr, on September 23 last year.
A 28-year-old woman was pushing her four-day-old baby in a pram across the dual carriageway near Beeches Road when they were hit by a car.
The mother was left with a serious head injury and multiple fractures and had to spend several days in hospital.
Rose, of Trinity Road, Aston, was arrested on Sunday at an address in Walsall.
He is due before Birmingham Crown Court on August 22.