The case is being investigated by the Mutual UFO Network (MUFON) after it was sent the footage and a witness report.
The man was in Lincoln, New Hampshire, in the US, when he recorded the odd video.
It appears to show a plane being folloed and caught up by a smaller object.
In a report to US-based MUFON, which is the world’s largest organisation dedicated to UFO and alien research, the unnamed man said: “I am told that military pilots train in the mountains around where I live and I’ve always enjoyed seeing them fly through.
“This happens all the time. Jets and helicopters are a common sighting.
“So I naturally saw the jet and did a double take, because there was something following it.”
But, the witness thought the object looked strange, and was possibly something the military built, that was different to a plane or jet.
He added: “I knew it wasn’t a jet because it was actually right behind one. The jet it was chasing left a long contrail behind it, but the UFO did not.
“The UFO was gaining on the jet. No helicopter could do that. I was blown away and luckily got out my phone in time to take a video.
“I watched the object gaining on the jet for about 10 seconds when I lost them in the trees.
“I felt I had witnessed something very hard to dismiss as a weather balloon or some obvious type of aircraft.
“Shortly after the jet and object left my range of sight I saw three more jets and one helicopter going the same direction – in my opinion chasing the UFO.
“I also got another video of those other aircraft. I would like to show the video to an aviation expert and maybe get an explanation. I’m uploading to MUFON hoping for answers.”
The footage was recorded at 7 pm on April 21, 2016, but it is now being investigated by MUFON
New Hampshire field investigator Breann Smith.
Roger Marsh, MUFON director of communications, said: “Please remember that most UFO sightings can be explained as something natural or man-made.”