The political game is the invention of Sue Lawless, a school librarian, who is trying it out with pupils at Holy Cross secondary in Lancashire.
Students play the game in groups of five, competing as candidates for the BNP as well as the Conservative, Liberal Democrat, Green and Labour parties.
Mrs Lawless said pupils could pick the party and "quite a few" at her school would choose the far-right group. "The BNP are trying quite hard in Chorley and the more working-class kids here would think that what it does is pretty good," she said. "It wouldn't be realistic to ignore it."
The librarian said she felt the BNP could get one or two seats at the next general election and that she had been disappointed she had not been able to visit its website for research because it had been blocked by the school intranet.
She described BNP policies as attractive superficially, but stressed she was a "floating voter" and saddened by its successes.
Pupils receive cue-cards describing the policies of their parties and give a brief talk to the others before first rolling the dice. They make their way around the board, collecting votes until they are elected as MPs. They then move to a second level where they work their way up to be leaders of their parties.
The Anti-Nazi League has condemned the game for legitimising the BNP. A spokesman said: "We would have thought that schools were the last place for this and that many teachers will be up in arms."
However, a spokeswoman for the Department for Education and Skills said games were a useful way to teach citizenship and that it trusted teachers to ensure discussions on controversial issues were carried out in a fair and balanced manner.
Tony Charnock, head of Holy Cross, said he believed the game in no way promoted the BNP and that he had not heard pupils expressing an interest in the party in his discussions with them.