The couple released a new video featuring previously unseen footage of the little girl playing happily with her family before her disappearance.
She dances around dressed in a fairy outfit, jokingly hits her father with a soft toy and speaks proudly of her new pink shoes.
The clips were mostly filmed around Christmas 2006, the last time the McCanns were together with all three of their children over the festive period.
Madeleine was nearly four when she vanished from her family's holiday apartment in Praia da Luz in Portugal on May 3 last year as her parents dined with friends nearby.
The new video shows her sitting on the stairs of the McCanns' home in Rothley, Leicestershire, flanked by her younger siblings, twins Sean and Amelie.
In the first recording of her speaking that has been made public, she encourages her brother and sister to copy her gestures, saying: "Clap your hands together and one, two, three."
Madeleine then holds up her new pair of shoes and says: "These are my shoes."
Behind the camera Mr McCann asks her what colour they are, and she answers: "Pink."
The little girl - who was three at the time - then leaps up from the stairs and dances around the wooden floor, waving her shoes and looking up at the light streaming in from a window.
The short film, which has Snow Patrol's hit song Chasing Cars as its soundtrack, also features a montage of clips of Madeleine.
She is seen turning over a Christmas present and pointing at the camera as a smiling Mrs McCann holds her.
Mr and Mrs McCann decided not to appear in the new video, but it includes a direct emotional appeal from them for assistance: "Christmas is a time for children. Please help bring our daughter back."
And it closes with the words: "This will be our second Christmas without our daughter. Please help us make sure we don't have a third."
McCann family spokesman Clarence Mitchell said: "Kate and Gerry do not wish to say anything further. They feel the video will speak for itself.
"This message is entirely focused on Madeleine, as it should be at this time of year.
"Kate and Gerry are still very much continuing a lot of hard work behind the scenes in the search for their daughter.
"This, they feel, is a timely and appropriate reminder that she is still out there and that somebody somewhere may still have that vital piece of information that may lead to her being found."
Mr and Mrs McCann will spend Christmas with their twins and close family and friends, but their spokesman acknowledged it will be a "difficult time of year".
Mr Mitchell added: "Producing a video like this is itself making it more difficult.
"But they are doing it because they believe Madeleine is still out there and they want that piece of information."
It has been a gruelling year for Mr and Mrs McCann.
The couple started 2008 with a cloud of suspicion hanging over them after Portuguese police named them as "arguidos", or formal suspects, in their daughter's disappearance.
They then marked a series of painful landmarks, in particular the first anniversary of Madeleine's vanishing on May 3 and her fifth birthday nine days later.
The McCanns were relieved when prosecutors announced in July that they were shelving the case and lifting the couple's arguido status.
But this was tempered by frustration that detectives were no longer actively investigating Madeleine's disappearance.
In August thousands of pages from the official Portuguese police files were made public, revealing the many different lines officers pursued in their 14-month inquiry.
Mr and Mrs McCann, who say they will believe their daughter is alive until given clear evidence to the contrary, have had the documents translated into English and are still painstakingly going through them.
It is understood they are being assisted by a small team of retired senior British police officers with case review experience.
The couple have only given one interview, to Portuguese newspaper Expresso, since their arguido status was lifted.
Mr Mitchell said this would not change until they had a specific message to communicate that would help the search for Madeleine.
:: The new video can be watched on the McCanns' website, www.findmadeleine.com
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