Question Time is one of the most well-known political programmes around.
Show bosses invite politicians and other experts to appear, and they are questioned by a studio audience about important political points and issues.
Protesters outside the BBC
Thursday is the first time a member of the BNP will take part. Lots of people are protesting about Mr Griffin's appearance outside the BBC building in London.
The BNP don't let anyone who isn't white join them. A court case is taking place at the moment to decide if this policy is legal or not.
During the case Mr Griffin said he would ask the other members of the BNP to change that rule, but that vote hasn't happened yet.
The BNP also doesn't like people from other countries moving to the UK.
But the BNP insists that doesn't mean it's racist - it says it's standing up for white people who were born in Britain.
Even other politicians are divided on whether Mr Griffin should be allowed on the show. Some think it's important that every single person has the right to be heard, whatever they are going to say.
Others are worried that he could say racist things when answering questions, and are even concerned that there could be a rise in racist attacks on people after the programme.
BBC bosses have said it's not their job to say if a politician should or shouldn't be on TV, whatever the views of their party.
They say that because the BNP won seats at the most recent European elections they have enough support to be involved in political programmes.
The Deputy director general of the BBC, Mark Byford, said: "They should have the right to be heard, be challenged, and for the public who take part in Question Time and the viewers to make up their own minds about the views of the BNP."