According to The Guardian, the organisation is unhappy about remarks made by Dara O'Briain and Brian Cox on the show.
During the programme, which aired on January 3, O'Brien allegedly said: "Let's get this straight once and for all, astrology is rubbish."
Cox reportedly replied: "In the interests of balance on the BBC, yes, astrology is nonsense."
The Astrological Association has now set up a petition on their website to complain about the comments, saying: "The Association will be requesting that the BBC make a public apology and a statement that they do not support the personal views of Professor Brian Cox or Dara O'Briain on the subject.
"We also request that the BBC will commit to making a fair and balanced representation of astrology when aired in the future."
Guardian writer Martin Robbins is now planning to pass on a counter-petition to the BBC supporting O'Briain and Cox.