The trio's mother had to be put down after suffering severe seizures, and two of her kittens also died.
Leeds Cat Rescue says the owner was "unable to cope" and the three surviving kittens were taken into the care of volunteers on Friday.
More than 30 kittens are now being looked after by Leeds Cat Rescue, which is run by volunteers who foster the cats until they can find a permanent home.
Vanessa Hill, rescue coordinator, posted a picture of the kittens on social media and said: "They're very little for their age but lively and so hopefully they'll soon start to thrive.
"These new additions take the number of kittens under 12 weeks to 32 which is simply ridiculous for the end of December!"
In August, Leeds Cat Rescue was unable to take in any more kittens after all its foster homes were completely full.
The team are 'desperate' for donations to help them keep up with the increasing demand of cats that need rescuing in West Yorkshire.
Anyone willing to donate to Leeds Cat Rescue can contact them via their Facebook page, on email [email protected] or on the phone number 07521 914398.