Billy Holmes was visiting the Cow and Calf rocks on Ilkley Moor on Friday afternoon when he spotted the creature.
He and his friends were around 20 metres away from the cat-like animal, which appears to be perched on a rock just above the precipice.
"I was walking across the Cow and Calf area as it was beautiful day, and there was this animal that was far more muscular than anything I had seen before. It was sort of lurking about and then got away as we got closer," said Billy, who lives in Hyde Park and studies at the University of Leeds.
"I reckon we were about 20 metres away and we saw some markings that were similar to that of a leopard or snow leopard. It literally looked like a huge cat. A group of men also saw it who were closer and were just as confused as us."
It's not the first time there have been rumours of big cats roaming the moorland above the West Yorkshire town.
Back in 2010, several residents of the nearby village of Burley-in-Wharfedale claimed they had seen one living wild.
The creature was described as 'black and puma-like' and was spotted by a couple on Hag Farm Lane. Other witnesses later came forward to say it was about the size of a labrador and could be seen in fields.
An Otley man claimed to have nearly crashed into a similar animal in Harden, near Bingley - and said that a gamekeeper he spoke to on Ilkley Moor seemed aware of the cat's presence.
Police logged a call back in April 2005 from a member of the public reporting a big cat sighting in neighbouring Menston.