Not having clinched a Test series since beating India 2-0 at home in December 2002, New Zealand have the chance to register a series victory against their unfancied opponents.
New Zealand, who were whitewashed 3-0 on their tour of England in May-June, should not have any problems against a side struggling to make an impression at Test level.
New Zealand have won both their previous Tests against Bangladesh by innings victories but skipper Stephen Fleming said they would have to work hard to win this time.
"We were playing at home then (in 2001) but this time we are playing on the sub-continent, which will not be easy," said Fleming, who warmed up for the Tests with a century in a three-day practice game.
"We haven't set ourselves any other target except to try and win the series," said Fleming, who will go back home after the Tests to rest an abdominal injury.
Left-arm spinner Daniel Vettori will lead the side in a three-match one-day series after the second Test in Chittagong next week.
Bangladesh, who have lost 27 of 30 Tests and drawn the remaining three since gaining Test status in 2000, also have an injury worry.
Captain Habibul Bashar, who missed the ICC Champions Trophy in England last month due to a finger injury, has yet to recover and his participation in the first Test will only be known on Monday.
"We hope Bashar will be able to play in the first Test. His presence will help the team morale a lot," said chief selector Faruque Ahmed.
"We want to persist with our combination and give the team a chance to settle down. We did reasonably well on our recent tours of the West Indies and Zimbabwe," he said.
Bangladesh salvaged a draw each against both the West Indies and Zimbabwe and have lost two of their four Tests this year.
Bangladesh: Habibul Bashar (capt), Rajin Saleh, Khaled Mashud, Javed Omar, Mohammad Ashraful, Manjurul Islam Rana, Tapash Baisya, Mushfiqur Rahman, Mohammad Rafique, Tareq Aziz, Nafees Iqbal, Hannan Sarkar, Alok Kapali, Alamgir Kabir.
New Zealand: Stephen Fleming (capt), Nathan Astle, Ian Butler, James Franklin, Hamish Marshall, Chris Martin, Brendon McCullum, Kyle Mills, Jacob Oram, Michael Papps, Mark Richardson, Scott Styris, Daniel Vettori, Paul Wiseman.