When Queen's Park was formed in 1867, the club initially played on the Queen's Park Recreation Ground at Crosshill, from where they took their name. In 1873 they moved to their first enclosed ground, naming it Hampden Park after a nearby street, Hampden Terrace. A grandstand and pavilion were erected over the next few years and the ground became a regular venue for international matches and cup finals, but in 1883 the club were forced to vacate the site to make way for the construction of the Cathcart Circle railway. After a year playing at Clydesdale Cricket Club's Titwood ground, a second Hampden was opened in October 1884. Whilst the club continued to attract major fixtures, they faced increasing competition as other Glasgow venues such as Celtic Park and Ibrox were developing their facilities more rapidly. To maintain their position in Scottish football, Queen's Park decided to purchase some farmland at Mount Florida, where the third Hampden was opened in 1903. Second Hampden was subsequently taken over by Third Lanark, who renamed it after their previous ground, Cathkin Park. 'Hampden' is one of the homes of football and celebrated its centenary on 31 October 2003. The stadium also houses the offices of the Scottish Football Association (SFA) and the Scottish Football Museum. Despite its large capacity and worldwide profile, it was owned by Queen's Park and leased by the SFA until 2020. It is the national football stadium of Scotland, the venue for all major cup finals and most Scotland international fixtures, and has hosted several continental showpiece events. Hampden Park was the largest stadium in the world until 1950, when the Maracanã in Rio de Janeiro was completed. Many of the record attendances in football were set at Hampden in the mid-20th century. After the release of the Taylor Report in the wake of the Hillsborough disaster, among other football tragedies, it was converted to an all-seater. Hampden's capacity following redevelopment was 51,866, although Queen's Park's average league attendance is around 600–700.
Lesser Hampden is a smaller ground to the west of the main stadium which Queen's Park traditionally used for training and reserve team or youth matches. In 2018, a deal was made for the SFA to purchase Hampden from Queen's Park upon the expiry of the lease in 2020 for a fee of £5 million, with the club intending to improve Lesser Hampden and play their matches there. In November 2019 the club announced plans to redevelop Lesser Hampden into a 1,774 capacity ground. As of August 2020, ownership of the main stadium had been transferred to the SFA and a new facility was under construction at Lesser Hampden. Queen's Park played their last match at Hampden on 20 March 2021, as their lease on the ground expired at the end of the month. They groundshared at the Falkirk Stadium for the rest of the 2020–21 season, and have agreed to share Firhill during 2021–22 until the work on Lesser Hampden is completed. The club released a revised plan in December 2021.