Accuse of

Anna said she thought Greta had eaten all the ice-cream.
Can I say in that way: "Anna accused Grata of having eaten all the ice-cream" ?
will it be grammatically right?

It's grammatically fine, but different from the original sentence.
1 ) The name is different. (typo?)
2 ) The meaning is different. A thought is not an accusation.

1) pardon, typo
2) so the correct answer is: accused Greta of eating. But I still can't understand why my answer is incorrect. And what about sequence of tenses?
she "said" - past simple tense, the situation of what had happened to ice-cream happened much earlier, then her friend began accusing her.

The gerund is much preferable to the perfect gerund. It has the preponderance of usage.
There is no sequence of tenses in your example.

"Anna accused Greta of eating all the ice-cream."

Compare with the following sentence. This one has a sequence because the actor is the same. The earlier action is the consumption of ice cream. The perfect participle is

Everything's clear now. Thank you!