Details about the father were kept blank when the birth was registered. But the baby was re-registered in December giving the father's name as Hugh John Mungo Grant.
"Anna is being supported by Hugh all the way. She lives in a very comfortable property in West London and knows Hugh is there for her," a source said.
Grant first's love child, a daughter was born in September 2011, to Chinese actress Tinglan Hong.
During an interview on a show, Grant had revealed that his daughter's Chinese name is Xiao Xi, meaning "happy surprise".
The actor and Hong reportedly rekindled their romance briefly in 2012 and in February 2013, it was announced that the pair became parents to a son named Felix Chang.