Helen Grant (34) caught a glimpse of a woman wearing a period dress through one of the hall's windows as she and partner David Nicholls walked around the gardens on Wednesday afternoon last week.
Within seconds of Helen seeing the woman, David ran to look through a window but she had disappeared.
This has left museum staff baffled as no-one wearing similar clothing was in the hall at the time.
An intriguing coincidence is that a painting of the late Isabella Johnson was taken from storage and hung in the room within a week or two of Helen's sighting.
Helen, of Stonegate, Spalding, said: "It did spook me. It didn't look like a ghostly figure. She just looked like a normal person.
"I think it was a ghost because of the dress she was wearing and the way she had her hair.
"I would like to find out who she was.
"People reading this might think that I am making it up but I swear on my life that I did definitely see it."
She described the woman as in her 30s or 40s and wearing a cream dress with blue flowers. It had a high neckline with a scallop effect. The woman had long dark hair and wore an Alice band.
South Holland District Council leisure and tourism manager Mark Croston said: "There is a feeling about the hall. It is quite a surreal, calm feeling. We do feel there is a lot of history and a lot of important things have happened here."
Assistant museum manager Louise Jacobsson said: "I am intrigued by the apperance. We do not have any documented ghost stories."
The section of the house where Helen spotted the figure was once the servants' side of the hall.
In the past Ayscoughfee was home to the Johnson family before becoming a school and housing Belgian refugees during the First World War.
Ayscoughfee Hall Museum will be opening to the public on Friday, June 30, after undergoing a major renovation project which has cost around £1m.

If you have seen a ghostly apparition in Ayscoughfee Hall call reporter Victoria Fear on 01775 765412.