Two kittens who have been named Tom and Jerry were found in a box
The numbers of unwanted animals being handed into the Bristol Dogs and Cats Home has risen since last year and the centre has now reached full capacity.
It is known as "kitten season" as the number of animals being handed in tends to rise as the breeding season closes.
The centre, which re-homes unwanted pets, now has more than 30 homeless cats, including a box of kittens dumped outside the centre's front door.
The RSPCA says it is the result of people failing to have cats neutered.
Four kittens were found in a box outside the clinic by staff. Two kittens have found homes but the remaining two, who staff have named Tom and Jerry, remain at the home.
Lee Coombs, of the Bristol Dogs and Cats Home, said: "We have reached full capacity and are very worried about our ability to take on any more animals that are unwanted.
"There is also a long waiting list for people who want to hand their cats and kittens over for re-homing.
"Anyone who believes they cannot afford to have their cat neutered only has to contact our RSPCA Veterinary Clinic to find out about our low-cost neutering schemes.
"There really is no excuse to end up with unwanted animals and dump them on our doorstep in a box. It is disgusting behaviour."