30 November 2015 Last updated at 16:35 GMT
Simon Whittaker, originally from Cheadle, posted his footage on Facebook saying: "Monarch A320 drifts off the centre line in cross winds at manchester airport and goes around."
Mr Whittaker, who used to fly planes himself, was on his way for a coffee at the Airport Hotel Pub when he noticed how the wind was affecting the incoming flights and began filming.
He said the weather was "absolutely treacherous" but that the pilot seemed "in control of the plane throughout the aborted landing". He said the winds were so strong that it was a challenge even keeping the camera steady.
Five planes were diverted from the airport on Sunday as a result of the high winds.
A spokeswoman said three planes were diverted to East Midlands Airport including two Monarch flights and another two went to Birmingham Airport.
The severe weather caused a roof on shops to be blown off in Greater Manchester, thousands of homes were left without power and trees were brought down.

Kenneth Feinberg, who was hired by GM to oversee its compensation fund, said he has received 251 death claims and 2,075 injury claims since August.
A total 100 of those claims were deemed eligible.
Potential claimants have until 31 January to submit paperwork.
Mr Feinberg, who previously administered claims for the 9/11 victims fund and those harmed by the BP Deepwater Horizon oil spill, has set up a website, for those looking to submit claims.
GM has set aside an estimated $400m (Â£256m) to pay out to claimants who were impacted by the defect, which involved ignition switches in millions of GM vehicles that could suddenly twist, thus turning the vehicle off.
GM has come under fire from US regulators and politicians for its failure to identify the problem earlier and alert consumers.
"Our goal with the compensation program has been to reach every eligible person impacted," GM said in a statement.
"Our focus isn't on numbers, but to continue doing the right thing for all those who lost loved ones or suffered physical injury.
"To that end, we accept Mr. Feinberg's determinations for the compensation program."
GM has been accused of hiding the defect for nearly a decade, despite multiple warnings from staff and complaints from consumers.
The firm has been forced to recall over 29 million cars worldwide this year - more than the total number of vehicles it sold in 2013 - although not all of the recalls were related to the ignition defect.
In April, GM's chief executive Mary Barra apologised for the fault when she appeared at a congressional hearing over the issue.
"I cannot tell you why it took years for a safety defect to be announced... but I can tell you that we will find out," said Ms Barra while testifying before a US House of Representatives panel investigating the issue.
In May, GM was fined $35m by the US highway safety administrator for its failure to issue a recall earlier - the maximum amount allowed by law.

The 27-year-old scored twice in eight appearances for the Hammers after joining from Velez Sarsfield.
But he had fallen out of favour at Upton Park following his summer move.
QPR boss Harry Redknapp said: "We're really pleased to bring Mauro in. He's a good footballer, someone with great ability who can play as a number 10."
A move looked on the cards after Zarate was quoted in the press as saying his manager Sam Allardyce refused to play him because he was signed by Hammers co-chairman David Sullivan.
Allardyce responded to that claim by saying the player "wasn't good enough" for West Ham.
After joining QPR, Zarate said: "I need to play and Queens Park Rangers have given me this chance to show what I can do."
He could make his Hoops debut in the Premier League at Burnley on Saturday.
A plane aborted its landing at Manchester Airport after winds of up to 70mph swept across the North West.
[NEXT_CONCEPT]
At least 42 people have been killed and 58 have been injured in General Motors vehicles that suffered from an ignition switch defect, according to the latest report by the claims administrator.
[NEXT_CONCEPT]
West Ham's Argentina striker Mauro Zarate has signed for Premier League rivals Queens Park Rangers on loan until the end of the season.