The band was created by guitarist Duncan Lloyd and is named after Máximo Gómez Park (also known as Domino Park), located in Little Havana, Miami. Initially, the four founding members played several small shows including Manchester's In the City, which showcases unsigned bands in the UK. In 2003, the band decided they wanted a frontman as the original singers, Archis and Duncan, wanted to focus on writing the songs. They found Paul Smith, who joined the band to sing.
The band's second release was a 7" single of their songs The Coast Is Always Changing and The Night I Lost My Head, recorded by Paul Epworth. After some time of doing gigs around their home town, Steve Beckett of the dance-electronic label Warp Records acquired one of these records and decided to sign the band to his label after also seeing the band perform at the Notting Hill Arts Club hosted by Creation Records founder Alan McGee.
In 2005, Maxïmo Park released their first album, A Certain Trigger, which sold over 300,000 copies and was nominated for the Mercury Prize in July 2005. In July, Maxïmo Park had the honour of being the first band to play the Ibiza Rocks festival on its opening event. In December 2006, the band were brought to Shanghai by Split Works and were one of the earlier big-name acts from abroad to play in China.
In August 2006, the band announced that they had started work on their next album, which was produced by Gil Norton and recorded at Rak Studios in St John's Wood in London. On 22 January 2007, the band announced that their second album, Our Earthly Pleasures, would be released on 2 April 2007 and would be preceded by the album's lead single, Our Velocity, on 19 March 2007. On 30 January 2007, the band released details of a tour to promote Our Earthly Pleasures, the tickets of which sold out within minutes of their release on 2 February 2007.
In October 2008, the band announced that they had started recording their third album in Los Angeles with the producer Nick Launay, known for his recent work with Nick Cave and Grinderman. The full track list of the album was announced on 11 March 2009. Quicken the Heart was released on 11 May, with the first single, The Kids Are Sick Again being released a week earlier. Tickets for a tour taking place in May 2009 sold out in record time. In 2010, they performed a new song called Banlieue, which ended up on their next album, The National Health. Their 2011 tour also had Banlieue in the set list, as well as another song which was to be on The National Health, Waves of Fear.
On 28 March 2012, Maxïmo Park announced the fourth album title as The National Health. The album was released on 11 June 2012.
On 15 November 2013, Maxïmo Park announced the forthcoming release of their fifth album. Titled Too Much Information, the album was released on 3 February 2014. The album was recorded and produced by the band, with additional production by The Invisible's Dave Okumu on the track Brain Cells. Recording originally started as an EP of 5 tracks in Sunderland, with help from Field Music's David and Peter Brewis, before turning into a fully formed album with the extra tracks recorded in the band's studio in Newcastle.
On 20 January 2017, Maxïmo Park announced their sixth album Risk to Exist via their website, following the debut of the title track and first single the night before on BBC 6 Music's Steve Lamacq Show.
