Batting first, Nepal scored 126 runs in 20 overs losing five wickets.
A 50-run opening partnership between Tamim Iqbal and Anamul Haque helped the hosts to chase down the target of 127 runs in 15. 3 overs losing merely two wickets.
Anamul Haque made highest 42 runs off just 33 balls for Bangladesh. Tamim scored 30 runs off 22 balls for the hosts.
All-rounder Shakib Al Hasan All-rounder Shakib Al Hasan who contributed 37 runs off just 18 balls hastened victory for his team with four sixes.
B Regmi bagged the only wicket for Nepal. Anamul was run out as the last Bangladeshi Batsman.
Al-Amin Hossain, who was adjudged man of the match, picked up two wickets while Mashrafe Mortaza and Farhad Reza claimed one wicket each to keep things difficult for Nepal batsmen with pace and spin for restricting to a modest total.
P Khadka scored highest 41 runs for Nepal while S Vesawkar made runs for his team.
Bangladesh won the toss and decided to field first in their second match of World T20 against Nepal which defeated Hong Kong by 80 runs in their first match of the tournament.
Bangladesh defeated Afghanistan by nine wickets in their first match.
There are 16 teams to participate for Men's title and 10 for Women's title, which will be played alongside.
The rest of the eight teams have been divided into two Groups which are Bangladesh, Afghanistan, Hong Kong and Nepal in Group-A while Ireland, Zimbabwe, Netherlands and United Arab Emirates in Group-B.