Sarah Jayne Ellis said she spotted the creature from her house near the River Aire in Castleford.
There was a similar sighting reported at a nature reserve in the town last year.
Ms Ellis said she thought the animal, which has been called the “Castleford Croc”, was around 3 or 4ft long and “looked real”.
She told YorkshireLive: “I thought 'that's a crocodile'.
“I was shutting the blinds in the bedroom when I saw it on the grass. I looked a couple of hours later and it was gone.”
Ms Ellis took a photo which she showed to her sister-in-law Kate Ellis Holmes, a deputy headteacher from Huddersfield, who said she was “in disbelief”.
“I thought it was bizarre and a really interesting story,” she said, adding: “It definitely looks like a crocodile.”
Ms Ellis said it should be investigated whether a crocodile really has been living in Castleford, especially given an earlier reported sighting further down the River Aire last year.
Wildlife photographer Lee Collings claimed to have seen a 4ft crocodile in the Fairburn Ings nature reserve on the edge of town in May 2020.
Mr Collings said the creature got away before he could capture it on camera but he insisted it was a crocodile, or perhaps an alligator.
“I'm not bothered about being ridiculed, I'm that confident about what I saw,” he told the Yorkshire Evening Post at the time.
The RSPB, which maintains Fairburn Ings, said they suspected the sighting to have been of an otter, which were not unknown to appear on the reserve.