Bangladesh, who take on New Zealand in the first of two Tests starting here from Friday, have won just one of their 53 Tests since being awarded Test status in 2000.
"We must win a Test now," said the 24-year-old skipper. "We need to show improvement in all departments and must put up strong opposition... like we did in the first one-day match."
Bangladesh upset New Zealand by seven wickets for their first-ever one-day win over the Black Caps in the opening match, before dropping the next two games to lose the recent series 2-1.
Ashraful has captained his side to Test series losses against Sri Lanka, New Zealand and South Africa since taking over last year.
In attack, the home team have left out pacemen Syed Rasel and Mahbubul Alam from the team, giving 21-year-old off-spinning all-rounder Naeem Islam a chance to shine on his Test debut.
Bangladesh will rely on their spinners with Abdur Razzak, Mehrab Hossain and Shakib Al Hasan -- all left-armers -- and Islam sharing the load on a Divisional Stadium pitch that is likely to favour slow bowlers.
New Zealand skipper Daniel Vettori said he had a good choice of bowlers.
"It will be a slow pitch, dust up a bit and crumble in the later stages. It is hot here but that is not a concern," he said.
"Our spinning options are well covered," said Vettori, who with off-spinner Jeetan Patel will supplement the bowling, alongside pacemen Iain O'Brien, Kyle Mills and Jacob Oram.
Jesse Ryder is expected to make his Test debut for New Zealand.
Vettori added he was looking for the team to up its game after a disappointing recent run, having gone down 2-0 to England in June.
"We are playing at 50 percent of our abilities and if we play to our full potential then we should win. We have not excelled in Tests recently," he said. The second Test will be played in Dhaka from October 25.