They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
Their technical consultant Stuart Law said the youngsters were keen to produce feats similar to those of Mashrafe Bin Mortaza and his men.
The youth team will mark Bangladesh's first semi-final appearance in a world event when they take on West Indies in the semi-final of the Under-19 World Cup on Thursday.
"They [Bangladesh U19] had great strides forward in the last couple of weeks. That’s due to the real success of the national team," Law said on Tuesday.