"These cats are a problem, they are all over town," she said.
"Out in the country we lead poison them but it would be difficult shooting them in Queen Elizabeth Park."
Councillor Gary Caffell said he had fielded many complaints over the stray cats.
The cats were diseased and unhealthy, he said, and it was not desirable to have children playing in the park near them.
"I believe it is quite a serious problem."
A report prepared for councillors by environment and planning manager Sue Southey said healthy trapped cats went to new homes but "there are only so many cats that can be rehomed".
"It's inevitable that some cats will have to be euthanised.
"Releasing them back into Queen Elizabeth Park is not considered to be an acceptable option," she said.
Mrs Southey said there were about five colonies of cats in the park, all being fed by "a group of people on a regular basis".
"The best result would be for council to stop the public from feeding these cats so they can be trapped," Mrs Southey said.
SPCA local president Val Ball said
five cats had been humanely trapped by a young Martinborough couple and were all in "excellent condition".
Mrs Ball said homes would now be sought for the cats, one of which was a little black kitten.