Animal rights protesters are urging the public not to visit Bobby Roberts Super Circus at the County Showground this week.
Around 30 members of the Captive Animal Protection Society (CAPS) demonstrated outside the Showground on the circus' opening night on Tuesday to raise awareness that a 56-year-old elephant is used in some of the acts.
Sally Koob, organiser of the protest, said: "This elephant, Anne, is the last to be used in a circus show in Britain and has extremely bad arthritis.
"Elephants used in circuses are chained on average for 22 hours every day. We are here making a peaceful demonstration to make the public aware of what happens to circus animals behind closed doors."
Six cars turned round deciding not to see the 7.30pm performance on Tuesday after talking with protesters at the entrance. Several other cars passing by beeped in support of their demonstration.
Sally continued: "The Born Free Foundation offered to buy Anne and release her in a safari park with other elephants. Bobby Roberts Circus turned it down because Anne is too valuable an asset for them to lose."
Anne's owners have disputed the claims that their circus elephant is being mistreated.
Moira Roberts, the circus' administrator, said: "Anne has been with us for 50 years and is part of our family. These protesters say she shouldn't be here but where else can she go? She is happy here. It is very upsetting.
"The Pembrokeshire Animal Welfare inspector from the county council has checked her and is highly satisfied with everything.
"People have the right to make up their own minds on whether they come to the circus or not. The circus has been part of Britain's heritage for hundreds of years. These people can demonstrate if they want to, they will not get a confrontation here, we do not allow it."
A Pembrokeshire County Council spokesperson confirmed animal welfare inspectors had carried out an inspection of the animals kept by the Bobby Roberts Super Circus at the Pembrokeshire Showground on Monday.
The spokesperson added: "Officers were satisfied that this circus was keeping animals to a high standard and that they were compliant with welfare regulations."
The Bobby Roberts Super Circus will be at the showground until Sunday.