His owner Lily told Newsround's website that Jimmy started stealing things last year, but this time his crime wave has been more serious.
She said he spent around two weeks taking stuff, although he's calmed down recently, just taking the occasional sock.
They know it's Jimmy who was stealing because a couple of times they spotted him coming into their garden with things in his mouth.
Flash shoes got taken
To help people get their stuff back, Lily and her husband put up posters explaining all about their cat burglar, and telling people to contact them if things were missing.
Some people have done so, including one lady whose posh shoe was returned just in time for her to wear to Ascot races the next day.
Luckily no one has been nasty when they've claimed their belongings, which is great because it means Jimmy won't get into any trouble.