Albuquerque in the 1930s was served by two private airports, West Mesa Airport and Oxnard Field. Around 1935 it was suggested that the city build a new public airport using WPA money. Having secured $520,500 USD in funding, Governor Clyde Tingley broke ground for the project on February 28, 1937. Albuquerque Municipal Airport opened in 1939 with two paved runways, a Pueblo Style terminal building designed by Ernest Blumenthal, and a massive hangar designed to accommodate the new Boeing 307.

The airport took on a new role in 1940 when it was designated Albuquerque Army Air Base, the precursor to today's Kirtland Air Force Base. The airport continues to share its runways with Kirtland, which also handles rescue and firefighting operations.

The present terminal was constructed in 1965 on a site just east of the original terminal. It has since been expanded twice, first in the late 1980s and most recently in 1996. The old terminal has been restored and currently houses offices of the Transportation Security Administration. It was added to the National Register of Historic Places in 1988.

ABQ's terminal, which was expanded to its present size in the late 1980s and again in 1996, encompasses 574,000 sq ft (53,300 m²). of space.

The airport has one passenger terminal that is designed in the Spanish-Pueblo style of architecture which houses two concourses and an area for commuter airline gates.

The count of passengers at the Sunport has seen an average per year increase of 2% over the last 15 years.

The airport's freight center moved 166,342,643 pounds of cargo in 2005.

The passenger terminal has free wireless internet access and electrical charging stations for passenger use.

Albuquerque International Sunport Airport covers an area of 2,039 acres (825 ha) which contains four runways. For the 12-month period ending December 31, 2006, the airport had 192,520 aircraft operations, an average of 527 per day: 38% scheduled commercial, 23% air taxi, 23% general aviation and 16% military. There are 322 aircraft based at this airport: 33% multi-engine, 30% single-engine, 18% military, 13% jet and 7% helicopter.

The airport has been considering closing the runway due to many reasons, mostly because of noise pollution of nearby subdivisions to the north. Because runway 17/35 intersects all three of the other runways, it has the highest risk of runway incursions; therefore air traffic control prefers not to use the runway unless absolutely necessary. The prevaling winds are from the west, and even during strong winds, the other runways can cover departure and landing. Currently, most of the runway's use is general aviation. Therefore, another option is to shorten the runway, but unfortunately that is costly.