"It took our country 26 years to get the first Test win," the New Zealand captain told reporters on Monday on the eve of the opening Test of a two-match series here.
"I think you (Bangladesh) will be quicker, with the number of people you have and the amount of talent you have."
Bangladesh have yet to win a match since gaining the Test status in 2000. They have lost 27 of their 30 Tests and drawn three -- two against Zimbabwe and one against the West Indies.
Fleming also urged cricket fans to be patient with Bangladesh, saying their biggest challenge was to make the game more competitive and entertaining by lifting performances at the highest level.
"People have to be patient," he said. "The challenge for Bangladesh is to play good cricket and the challenge for the ICC (International Cricket Council) is to be patient within its means."
The ICC is considering a proposal to restrict Bangladesh and Zimbabwe to home Test matches alone after their inability to compete with opponents on equal terms in recent years.
Fleming said it was necessary for Bangladesh to produce a few good results to avoid criticism from other Test-playing nations.
"If Bangladesh do not have a couple of good results, other Test-playing nations are going to be critical. That happens to any side. The world is looking for the development of cricket in Bangladesh," he said.
The South Asian minnows are likely to go into the match without captain Habibul Bashar, who is recovering from a thumb injury sustained during practice in August.
Bashar is Bangladesh's leading scorer, with 2,079 runs in 30 Tests with three hundreds and 17 half-centuries.
New Zealand are seeking their first Test series victory since beating India at home in 2002. They have won both of their previous two Tests against Bangladesh in 2001, but Fleming said his team would not find it easy this time.
"We then played at home, but this time we are playing on the sub-continent which will not be easy," said Fleming, who will return home after the Test series to rest an abdominal injury.
Left-arm spinner Daniel Vettori will lead the team in a three-match One-day series after the second Test in Chittagong next week.
Bangladesh (from): 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 (from): Stephen Fleming (capt), Nathan Astle, Ian Butler, James Franklin, Hamish Marshall, Chris Martin, Brendon McCullum, Kyle Mills, Jacob Oram, Mark Richardson, Scott Styris, Daniel Vettori, Paul Wiseman, Matthew Sinclair.