The organisation issued the warning after a branch in Chichester recently welcomed a 10-week-old puppy that had unexpectedly been given as a gift earlier this month.
The Border Collie, named Nanna, was cared for at the RSPCA's Mount Noddy Animal Centre and is now being looked after by a staff member from the center throughout the Christmas season.
Jess O’Connor, from the centre, said: “A man brought Nanna as a surprise Christmas present for a family member. But when Nanna arrived it upset her other dogs and she found it unmanageable so she contacted us for help.
“She’s such a sweetheart and has settled into her foster home really quickly. She loves to snuggle up with her foster sister, Labrador Rosie, and she’s quickly learning lots of new tricks.
“Belly rubs are her favourite thing and she spends her days enjoying long naps and has started toilet training with her foster carer.”
The RSPCA is hoping Nanna’s sad story will highlight why it’s not a good idea to buy someone a pet as a present.