The Duke and Duchess are expected to have their baby in July and Annabel is hoping the baby will be born on her birthday.
In her letter she wrote: "Congratulations that you're having a baby and I heard that your baby is born in July and my birthday is in July, too."
Annabel, a St Mary's School pupil, took her royal letter to school yesterday to show her friends who she said were all excited.
Her mother, Susannah Tucker, said Annabel loves princesses but only realised just how excited she was after telling her grandparents the news.
"'I got mail from a real princess' she said," Ms Tucker said.
She said Annabel is planning to make the Royals a card when their baby is born and hopes it will be a girl.
"When she wrote the letter I don't think she thought they were going to write back, I don't think it entered her head that she could get a reply," Ms Tucker said.
"It's pretty cool though that they do reply because you think how many kids from all round the world would send them letters."
Ms Tucker said she will be framing Annabel's letter.