West Midlands Police said the six suspects aged between 21 and 37 were arrested Wednesday under the Terrorism Act.
They are accused of belonging to National Action, which was banned in 2016. At the time it was the first far-right extremist group outlawed in Britain, AP reported.
Police are searching several properties in relation to the arrests.
The six suspects have not been charged or identified. They are being questioned by counter-terrorism police.
Police say the arrests were pre-planned and there is no threat to public safety.