Dear Heidi, Please consult with the book 'English Grammar in Use' by Raymond Murphy , Unit 66, p 132

there's a little difference afraid to (do): for things that are intentionally, you can choose to do them or not ''James was afraid to tell his parents what had happened'' afraid of (doing): for things that can happend like an accident '' I don't like dogs, I'm always afraid of being bitten''

1) Afraid to do: You can use it when you have a real fear to do something. For example: a) I'm afraid to tell him something wrong( I do not want to tell him something wrong because I'm afraid) b) I'm afraid of telling him something wrong( I'm afraid because I might tell something wrong) So the first sentence shows that you're afraid to do and the second shows that you have the feeling of fear to do something or some actions can happen which could make you feel afraid.

Hi Helen, there is no difference in meaning between the two phrases. 'Do not be afraid to do this' is equivalent to 'Do not be afraid of doing this.'