The airport was built on 28 March 1936 during Japanese rule with its origins as a Japanese military airbase, the Taihoku Airfield (Japanese: 臺北飛行場, Hepburn: Taihoku Hikōjō), also known as Matsuyama Airfield (松山飛行場). In 1937, Matsuyama Airfield was occupied by the Japanese Navy's Kanoya Air Group and its Type 96 G3M bombers for bombing positions on Chinese positions. On August 14, 1937, an 18-bomber mission launched from Matsuyama Airfield targeted Jianqiao Airfield in Zhejiang Province and Guangde Airfield in Anhui Province, both in China. The raid was intercepted by Chinese fighter aircraft, resulting in the loss of four bombers without any casualties on the Chinese side. This date was later celebrated as Air Force Day in China. In 1944, the Japanese Army's 37th Kyoiku Hikotai, a training unit equipped with Ki-61 fighters, was established at Matsuyama. Many of its instructors later engaged in combat against American forces over Taiwan and Japan during the war's final months. From March to August, 1945, the US Army Far East Air Forces bombed the airfield, with the last mission on 24 August using B-24 heavy bombers.

After World War II, in 1946, it was taken over by the Republic of China Air Force, and renamed to Songshan Airport. Before the end of the Chinese Civil War and the establishment of the People's Republic of China, the airport provided flight routes between Shanghai and Taipei, occasionally via Fuzhou.

Shared military and civilian use—both domestic and international—began on 16 April 1950 in the reconstructed Civil Aeronautics Administration Taipei Airport (交通部民用航空局台北航空站). Domestic destinations have been Kaohsiung, Hualien, Taichung, Penghu, and Tainan. The first international destinations were Seattle, Tokyo, Busan, Manila, Bangkok, and Hong Kong. The first international airlines included Northwest Airlines, Pan Am, and Hong Kong Airways (now Cathay Pacific). Later, the airport became too small to handle an increased number of passengers, even after a series of expansions. This later worsened when new wide-body jets became common at the airport. Therefore, all international activities were relocated to Taoyuan International Airport (then known as Chiang Kai-shek International) after its inauguration on 26 February 1979. Consequently, the passenger load at the airport dropped from 6.2 million in 1978 to 2.9 million in 1979 (a 53% decrease). At its peak in 1997, the airport handled over 15.3 million passengers annually.

Service to Taichung and Chiayi was stopped in mid-2007 after the load factor dropped significantly due to the Taiwan High Speed Rail's start of revenue service in January 2007. Passenger volume decreased from 6.7 million in 2006 to 4.4 million in 2007 (a 34% decrease). Also due to the opening of the high speed rail line, on 1 March 2008, Uni Air suspended its service to Kaohsiung, while Far Eastern Air Transport suspended its service to Tainan. TransAsia Airways decided to stop flights to Tainan and Kaohsiung after 1 August 2008.

In early 1999 when the construction of Taipei 101 had just started, Taiwan's Civil Aeronautics Administration changed this airport's certain SID and STAR procedures to avoid possible collision with the building. The 677-meter Fuxing North Road Underground Passage (復興北路車行地下道) was constructed between 1997 and 2006 under this airport's runway to link the north and south side of this airport.

Regular cross-strait charter flights to China started on 4 July 2008, with Songshan receiving the majority of flights. Direct flights to China were an issue of contention. Then-mayor Ma Ying-jeou had been pressing to make Songshan Airport Taipei's main International terminal, citing that its location close to the city center would make it preferable for business travelers. However, building height restrictions around the airport raised concerns about flight safety, blocking of radio communications, noise pollution, and a reduced number of flights.

The continuing growth of Taipei City means that Songshan airport is situated in the heart of downtown Taipei. Compared to Taiwan Taoyuan International Airport, Songshan Airport saves travelers about 30 minutes due to its location inside Taipei City's central business district, but the city suffers from the noise, pollution, restrictions on urban planning, and traffic congestion the airport brings about. In the 2002 and 2006 Taipei Mayor Election DPP candidates Lee Ying-yuan and Frank Hsieh both proposed the plan to close Songshan Airport, and developed its land into road, huge park, detention basin and sports arena, since the Taiwan High Speed Rail could quickly take up the traffic load between Taipei and western Taiwan cities, and the remaining service to outlying islands and eastern Taiwan could be easily taken over by the Taiwan Taoyuan International Airport after the completion of the Taoyuan International Airport Access MRT System by the end of 2016. Also, the MRT system will make the international potential of Songshan airport less attractive.