"Our bowling attack is reasonably good. If we can post a good total, it will not be impossible to win one or two games in the one-day series," Ashraful told reporters on Wednesday.
Bangladesh will also play two Tests on the tour, but Ashraful said his side's initial focus was on the three-match one-day series, which begins in Auckland on Dec 26, before matches in Napier (Dec 28) and Queenstown (Dec 31).
"We are not too concerned about the Test matches right at this moment. First of all we will try to put a good show in the one-day series," said Ashraful.
"If we can do well in the one-day internationals, the spirit in the Tests will be high automatically."
"No doubt it is going to be a tough tour ... but we have confidence in ourselves. We are not going to be easy prey for New Zealand."