What form is Frankenstein written in?

It is a frame story. In fact it can be considered to be a double frame story as everything is related through Captain Robert Walton who gets everything from Doctor Frankenstein. At times it can be considered a triple frame story as the monster also has passages when he is relating things through the doctor.

Also the story can be considered an epistolary as Captain Walton is telling the story in a letter to his sister.