The orders will be worth about $1,100bn (pounds 680bn), claims Boeing in its annual report on the market for new passenger aircraft.
Demand for new airplanes would be driven by a 4.9 per cent average annual increase in air traffic, Boeing said.
"The industry continues on the upswing," said Bruce Dennis, vice president for marketing at Boeing's commercial airplane group. "It looks good out there."
However, Boeing's forecast for the increase in air travel was slightly less optimistic than it was last year.
The company predicted then that air travel would grow 5.1 per cent a year through to 2015, compared with yesterday's revised forecast of 4.9 per cent to take account of slower growth in the US.
Boeing's orders have been improving since 1995, when airlines started to replace ageing fleets. Airlines have also been increasing the size of their fleets.
Orders for Boeing aircraft almost doubled to a record $53bn in 1996.
The world's largest commercial airplane maker took orders for 717 aircraft last year, compared with 346 in 1995 and just 120 in 1994.
Mr Dennis said the Seattle-based airplane maker would see strong orders again this year, though he declined to be specific. Boeing will produce 40 airplanes a month in the fourth quarter of this year, its highest output.
There are about 11,500 jetliners flying today, 7,000 of which were made by Boeing. The world's fleet will grow to 23,600 passenger and cargo planes by 2016.
That number accounts for older planes that are retired from service.
The biggest demand for new aircraft will come from Asia, where Boeing expects air travel to grow 6.6 per cent a year, compared with 3.1 per cent in the US.
Airlines in the Pacific will account for 33 per cent of the $1,100bn that will be invested in new planes in the next 20 years.
There would be more demand for smaller airplanes, carrying between 100 and 240 passengers, Boeing said.
That segment of the market will account for 43 per cent of all aircraft investment. The smallest market will be for planes that hold more than 400 passengers, including Boeing's 747, the world's largest commercial aircraft. About 18 per cent of all investment will be for larger planes.
A few weeks ago, Boeing cancelled work on two larger versions of the 747 capable of carrying more than 500 passengers.
Boeing said the small size of the market didn't justify spending as much as $7bn developing the planes.