Your sentence is fine, Ilham. Home in your example is behaving like an adverb expressing direction. We do not need a preposition with home when it is used with any verb referring to direction: ...

There are time prepositions (before, after, during, until), place prepositions (around, between, at, against) and direction prepositions (down, up, across). Place prepositions revolve around the ...

“From”, “at”, “since” or “around” – prepositions like these help us to locate things. They point us in the right direction – in time or place, for example. But it is not always as simple as it seems.