West Yorkshire Police made the discovery after executing a search warrant at Kenneth Brockley's home in July 2019.
Leeds Crown Court heard officers arrested the 71-year-old and seized computer equipment.
The defendant insisted he had done nothing wrong and denied searching for indecent images of children.
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The equipment was searched and 21 illegal images and movies were recovered.
An image depicting bestiality was also found.
One movie was at category A - the most serious kind.
It was 26 minutes long and depicted a child being abused by a man and a woman.
Brockley, of Blakeney Grove, Hunslet, pleaded guilty to three counts of making an indecent image of a child and one of possessing an extreme pornographic image.
Stephen Welford, mitigating, said Brockley pleaded guilty to the offences at an early stage and has no previous convictions.
Mr Welford said his client has been married for 50 years and had worked hard all his life up until retiring.
The barrister said Brockley had been assessed as a low risk of re-offending by the probation service and could be dealt with by a sentence served in the community.
Brockley was given a six-month prison sentence, suspended for 18 months.
Read more: Cocaine worth half a million pounds found in secret compartment of 62-year-old man's Honda Civic on M62 in LeedsHe was also ordered to complete 15 rehabilitation activity requirement days and pay £340 court costs.
Brockley was told he must go on the sex offender register for ten years.
He was made the subject of a ten-year sexual harm prevention order.
Judge Simon Phillips QC said: "At 71 years of age it is something of a personal tragedy for you and your family that you are before the court having pleaded guilty to these serious matters.
"You have only yourself to blame for the situation you find yourself in."