The airport has been named United Airport (1930–1934), Union Air Terminal (1934–1940), Lockheed Air Terminal (1940–1967), Hollywood–Burbank Airport (1967–1978), Burbank–Glendale–Pasadena Airport (1978–2003), and Bob Hope Airport after comedian Bob Hope (since 2003 as the legal name). In 2017, it was rebranded as Hollywood Burbank Airport due to the lack of recognition of Bob Hope Airport's geographic region.

United Aircraft and Transport Corporation (UA&T) was a holding company created in 1928 that included Boeing Aircraft and United Air Lines, itself a holding company for a collection of small airlines that continued to operate under their own names. One of these airlines was Pacific Air Transport (PAT), which Boeing had acquired because of PAT's west coast mail contract in January 1928. UA&T sought a site for a new airport for PAT and found one in Burbank. UA&T had the benefit of surveys that the Aeronautics Department of the Los Angeles Chamber of Commerce had conducted starting in 1926 to identify potential airport sites.

It took UA&T a year and the cooperation of the city to assemble the site. The 234-acre (95 ha) site was rife with vines and trees and the ground had to be filled and leveled, but it had good drainage, a firm landing surface, steady winds, and good access to ground transport. Construction was completed in just seven months. In an age when few aircraft had brakes and many had a tail skid instead of a wheel, runways were not usually paved; those at Burbank had a 5-inch-thick (130 mm) mixture of oil and sand. There were no taxi strips, but the designers left room for them. Two of the runways were over 3,600 feet (1,100 m) long; a third was 2,900 feet (880 m); all were 300 feet (91 m) wide. These were generous dimensions, and the site had room for expansion.

United Airport was dedicated amid much festivity (including an air show) on Memorial Day weekend (May 30 – June 1), 1930. The airport and its handsome Spanish Revival-style terminal was a showy competitor to nearby Grand Central Airport in Glendale, which was then Los Angeles' main airline terminal. The new Burbank facility was actually the largest commercial airport in the Los Angeles area until it was eclipsed in 1946 by the Los Angeles Airport in Westchester when that facility (formerly Mines Field, then Los Angeles Municipal Airport) commenced scheduled airline operations.

The Burbank facility remained United Airport until 1934, when it was renamed Union Air Terminal. The name change came the same year that federal anti-trust actions caused United Aircraft and Transport to dissolve, which took effect September 26, 1934. The Union Air Terminal moniker stuck until Lockheed bought the airport in 1940 and renamed it Lockheed Air Terminal.

In March 1939, airlines scheduled sixteen departures a day out of Burbank: eight United Airlines, five Western Airlines and three TWA (American Airlines' three departures were still at Glendale). Airline flights continued even while Lockheed's extensive factories supplied the war effort and developed military and civil aircraft into the mid-1960s. The April 1957 OAG lists nine weekday departures on Western, six on United, six on Pacific Air Lines, one on TWA and one on American Airlines (a nonstop to Chicago Midway Airport). Pacific Southwest Airlines (PSA) had 48 Douglas DC-4 departures a week to SFO and SAN. PSA did not fly out of LAX until 1958.

In 1958, Transocean Air Lines Lockheed Constellations flew to Honolulu three times a week; twice a week a Constellation flew Oakland - Burbank - Chicago Midway Airport - New York Idlewild Airport (now JFK Airport) - Hartford. In summer 1962 PSA flights to San Francisco and San Diego were all Lockheed L-188 Electras, a total of 32 departures a week from Burbank.

Jets arrived at Burbank in the late 1960s: Pacific Air Lines flew Boeing 727-100s nonstop to Las Vegas and San Francisco and one-stop to Eureka/Arcata. Pacific Southwest Airlines (PSA) flew 727s to the San Francisco Bay Area and San Diego. Hughes Airwest (previously Air West) flew Douglas DC-9-10s and McDonnell Douglas DC-9-30s nonstop to Las Vegas, Phoenix, Salt Lake City and Denver with one-stop DC-9s to Houston Hobby Airport.

Hughes Airwest even operated one-stop DC-9s to Grand Canyon National Park Airport near the south rim of the Grand Canyon. In 1986 United Airlines Boeing 767-200s flew nonstop to Chicago O'Hare Airport. The 767 was the largest passenger airliner ever to serve Burbank. AirCal McDonnell Douglas MD-80s flew nonstop to the Bay Area and direct to Lake Tahoe.

In 1967, Lockheed renamed the facility Hollywood–Burbank Airport. In 1970, Continental Airlines began Boeing 727-200 flights to Portland and Seattle via San Jose and also flew the short hop to Ontario. Continental later offered flights to Chicago via Ontario. Continental went on to serve Denver with nonstop Boeing 727-200s from BUR. Alaska Airlines began serving Burbank in 1981 with Boeing 727-100s and 727-200s flying nonstop and direct to Seattle and Portland, which was Alaska Air's first service to southern California.