The Facebook group 'Tesco employees could rule the world' included posts describing customers as rude, smelly and stupid.
Comments on the site included moans about customers asking them questions and querying prices. The group, which has now been taken down, has around 2000 members, although only around 60 took part in the discussion about customers.
Complaining about being asked whether they were a member of staff, one member of the group said: "No, I just think the Tesco uniform is the height of fashion. In fact I saw it in Vogue only last week. Of course, I work here you moron."
Another, discussing his reaction when asked by a customer for the location of a particular product, said his instinct was to say: "Give me your shopping list you senile old cow, and I'll do your shopping for you. Just leave me alone."
Tesco said it appreciated Facebook was a popular site, but said that "if staff have gone too far we will investigate and take appropriate action".
The store refused to discuss the site any further. A spokesman said: "This is about individuals and even if something did come out of an investigation we wouldn't comment on it."
Tesco's problems with Facebook mirrors a similar problem faced by Virgin Atlantic last year. A group formed of staff posted insulting comments about the airline and its customers.
Group members called customers "chavs" and questioned Virgin Atlantic's safety standards. Thirteen staff were eventually sacked as a result of an investigation.
Additionally last week The Grey Coat Hospital School, a London girl's school, suspended 29 of its pupils after they posted insulting comments about a teacher.