The ITV period drama was renewed for a second series back in October and filming on the new episodes has now begun.
"The new scripts are as good if not better than the first series," Bonneville told What's on TV. "There are some great adventures on the way with new characters, twists and turns."
He added: "It's also set in the First World War, so the weight of that wears down on the house, which becomes a convalescent home at one point, so there's a whole new atmosphere."
The actor, who plays the Earl of Grantham, admitted that "the stakes are higher" for the new run following the huge success of the first.
"The public has embraced the show in a way that none of us ever predicted and it's very gratifying," he said. "It genuinely became a Sunday night fixture for families."
Bonneville added that he was also surprised by the show's international success.
"You think you are doing something which is very parochial and very English and nobody will get it," he revealed. "But the quality of the writing means that everyone can understand the themes and the way these characters interact."
The second eight-part series of Downton Abbey will air on ITV1 later this year.
> The return of Downton Abbey