The Duchess of Cambridge was admitted to hospital on Saturday in the early stages of labour, a media report said.
Catherine was admitted to the Lindo Wing at St. Mary's Hospital in London where her first child, Prince George, was born in July 2013, BBC reported.
The new baby will be fourth in line to the throne, behind his or her grandfather Prince Charles, father Prince William and brother Prince George.
Kensington Palace said "labour is progressing as normal" for the duchess, who was taken to the hospital accompanied by husband, Prince William.
"My best wishes to the Duchess of Cambridge, who is having her second child today. The whole country will wish her well," Prime Minister David Cameron tweeted.