Carlisle Airport would also become a freight terminal and the base for transport firm Eddie Stobart, currently located in the city itself.
Airport director Richard Gordon said up to 170,000 passengers could be using the airport within six years if the plans are approved.
He argued that the airport is losing money and needs to develop to make a profit. He warned that Eddie Stobart will move elsewhere if the airport option is blocked.
Council leader Mike Mitchelson said: "It is important to keep the firm here because there are good jobs attached." He said he backs airport growth as part of the area's economic strategy, which includes expanded business and residential provision.
Friends of the Earth objects to the plans. Its aviation campaigner Richard Dyer said Eddie Stobart could move to the airport without its expansion, adding that local residents fear increases in traffic and noise levels.