Works are currently being carried out to fell diseased ash trees lining both sides of the dual carriageway.
West Sussex County Council says that it needs to close parts of the road for safety reasons while felling takes place.
The A24 southbound at Worthing Road will close overnight from February 1 - 4
The A24 southbound Horsham bypass will close overnight from February 14 - 23.
Diversion signs will be in place.
The council says the felling is essential as the ash trees, suffering from dieback, could pose a risk to drivers with branches potentially falling into the road.
Ash dieback is predicted to kill a high number of Ash trees across the country.
A council spokesperson said: “Removing infected trees is the best way to avoid spread of the disease.
“We have a tree planting policy to ensure we maintain a high number of trees in West Sussex.”
The disease has the potential to kill 95 per cent of West Sussex ash trees over the next 10–20 years.