Jamie Blake, 19, put the stray, called Buddy, into the microwave because he said it was telling him his mother's ex-partner, who is dead, was injecting her with heroin, a court heard.
Bury St Edmunds Magistrates' Court heard Blake had befriended the cat while staying at John Room House sheltered accommodation in Thetford, Norfolk, the 'Daily Mail' reported.
Prosecutor Sarah-Jane Atkins argued that he kept the cat in his room to give him company at night and fed it cheese and tuna.
Blake, however, claims the cat began arguing with it before forcing him to put it into the microwave on September 27.
Atkins told the court that the teenager had then laughed to friends about how he microwaved a cat to death and told other residents about it but initially no one believed him.
"Apparently he was laughing about this to other residents, saying he had put it in the microwave for three minutes, killing it and appeared to be quite jovial about the situation," she said.
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Fran Lewis from the probation service said Blake had a drug problem which may have contributed to his mental health issues.
After fur was spotted near Blake's room, CCTV footage was investigated and it showed him picking the cat up by the scruff of its neck and taking it to his room.
The CCTV then showed Blake leaving his room with a carrier bag which appeared to have the dead creature in it and then disposing the oven the next day.
Soon after, staff from John Room House found the cat and the microwave in the bin area.
Blake will be sentenced in court for killing the cat on October 30.