The sergeant, who has not been named, was off-duty when he saw the figures standing in a field near Silbury Hill, and stopped his car to investigate.
However, as he approached the 'men' – all over 6ft tall with blond hair – he heard "the sound of static electricity" and the trio ran away ''faster than any man he had ever seen''.
The officer returned to his home in Marlborough, Wiltshire, and contacted paranormal experts and told them he had spotted a UFO.
Wiltshire Police has refused to comment on the incident, saying it is a ''personal matter'' for the officer involved.
Crop circle researcher Andrew Russell, who is investigating the bizarre sighting on behalf of the officer, described the moment his sighting was made.
He said: ''At first he thought they were forensic officers as they were dressed in white coveralls. He stopped his car and approached the field.
''The figures were all over 6ft and had blond hair. They seemed to be inspecting the crop. When he got to the edge of the field he heard what he believed to be a sound not dissimilar to static electricity.
''This crackling noise seemed to be running through the field and the crop was moving gently, close to where the noise was.
''He shouted to the figures who, at first, ignored him, not glancing at him. When he tried to enter the field they looked up and began running.
''He said; 'They ran faster than any man I have ever seen. I'm no slouch but they were moving so fast. I looked away for a second and when I looked back they were gone.
''I then got scared. The noise was still around but I got an uneasy feeling and headed for the car. For the rest of the day I had a pounding headache I couldn't shift.''
The bizarre incident occurred on the morning of July 6 this year as the police officer was driving.
The officer claims the three figures were examining a crop circle, which had appeared several days earlier, when he stopped his car and began walking towards them.
However, the mysterious beings disappeared when he ''looked away for a second'' and he contacted UFO experts after witnessing other paranormal activity.
A spokesman for Wiltshire Police said: ''The police officer was apparently off duty when this happened so we have no comment to make because it is a personal not a police matter.''
Crop circle expert Colin Andrews, who investigated the incident alongside Andrew Russell, said he is ''convinced'' by the police officer's story.
He said: ''I am quite convinced the officer had an experience that day and one that we have not fully explored.
''I think with the unusual movement of the being and the poltergeist experiences there is too much additional information to say that is something in nothing.''