Nats Prestwick expects to handle more than 250,000 flights during the peak holiday season this year - an increase of 15,000 on last year.
The company has announced a Â£600m investment in a new computer system.
But it says government support is needed to improve the network of "ageing" flightpaths.
Paul Peers, head of development at Nats Prestwick, said: "We are predicted to have the highest amount of traffic we have ever had for a summer period this year.
"We are expecting to have around 15,000 more flights just in July and August compared to last year.
"We are ready for that and our controllers have been doing a great job up to this point making sure that we minimise the delays that people see and making sure that we keep people safe in the skies.
"We have been preparing for this since November, so the summer doesn't come as a surprise to us, and we have a series of events to make sure our controllers are ready for the summer traffic.
"Indeed, this year, the build-up in traffic has helped us with that because we've had record days already that our controllers have dealt with extremely well.
"But one of the big challenges for us is the design of the airspace in the future and the traffic growth."
He added: "We are investing over Â£600m over the next few years in the technology systems.
"In fact, at the Prestwick centre we are proud to say that we have the first version of iTec, our new flight data processing system, in operation already and that is the first in the UK.
"The skies are getting fuller every year and we are expecting to see increased traffic growth.
"But if you think about the airspace as effectively motorways in the sky, if you think about 1970s motorways with today's car traffic, we are in a similar scenario.
"We are going to have to redesign our airspace and we are going to need government support to make sure we can do that in the right way."
The national air traffic service (Nats) has said a "massive" programme of modernisation is needed to keep up with demand for air travel.