Standing in his way will be world number one Novak Djokovic, who won the title at SW19 two years ago.
Here, Sports Mole has looked back on how the Brit has fared during his previous six outings at a Major final.
US Open, 2008
To be fair to Murray, not too many people expected him to challenge for the title at Flushing Meadows. He was just 21 and had never previously gone beyond the last eight at any Slam.
He stunned the tennis world, though, by recording a four-set win over Rafael Nadal in the semis, but Roger Federer in the final proved a step too far. The Swiss was on the top of his game and recorded a 6-2 7-5 6-2 win.
Australian Open, 2010
In terms of Grand Slams, 2009 was a disappointing year for Murray. He started 2010 in positive fashion, though, seeing off Marin Cilic in the semi-final to reach the final of the Aussie Open.
There was more expectation on Murray this time around, but Federer would again prove to be too good for the Scot as he triumphed 6-3 6-4 7-6.
An emotional Murray said at the end: "Got great support back home the past two weeks. Sorry I couldn't do it for you tonight. I can cry like Roger - it's just a shame I can't play like him."
Australian Open, 2011
Twelve months fast forward and Murray was back in the final at Melbourne. A further positive was the fact that he did not have to contend with Federer, who had been knocked out by Djokovic in the semis.
The Serbian was at his classy best in the final, though and crushed Murray 6-4 6-2 6-3.
At this point, Murray was yet to win a set from his three Grand Slam final appearances.
This was surely going to be the one. At last there was a Briton in the final of the men's singles at Wimbledon; surely Murray was going to end the wait for a first Grand Slam victory since 1936?
Giddiness set in among the Brits as he claimed the first set against old foe Federer 6-4, but the former world number one kept his composure and eventually won through 7-5 6-3 6-4.
This one really stung Murray. The tears flowed as he made his post-match speech to the crowd. He had won a set at last, but big question marks had surfaced as to whether or not he was always going to be the nearly-man.
US Open, 2012
When Murray met Djokovic in New York last September, it had the feeling of 'now or never' for the then 25-year-old. He had been working with coach Ivan Lendl since the start of the year - would the Czech's intervention come to fruition?
He took the first two sets 7-6 7-5, but when Djokovic responded 6-2 6-3 to level up proceedings, every Murray supporter would have feared the worst.
However, on this occasion he was not to be denied and rallied to win the decider 6-2 in an epic contest that lasted six minutes shy of five hours. Britain's 76-year wait for a Grand Slam champion was over.
Murray was too tired to cry this time, he could barely walk!
Australian Open, 2013
By the time that this year's Slam in Australia had swung around, Murray and Djokovic were widely regarded to be the best two players in the world. They proved that in Melbourne as they both reached the final, with Murray having overcome Federer in five sets in the last four.
There was to be no repeat of US Open heroics, though. The first set was won on a tie-break by Murray, but Djokovic responded by claiming a breaker of his own during the next set.
From then on it was all about the Serb, who turned on the style and won through 6-3 6-2.