As President Elect, he is eligible to use government aircraft for transition business (like this trip). However, I suspect his plane is more comfortable.
Once he is President, he is required by law to use government aircraft with certain secure communications capabilities. He will not be allowed to use his own plane.
Obama got a lot of flack for the cost of his travel, some justified, but some is unavoidable. No President can travel by private or commercial aircraft. The downside of the Presidency is that you live in a gilded cage.
He was telling me when a president does an overseas visit, the Secret Service has to fly heavy transport planes (C-5 Galaxies) with the entire motorcade onboard (Tahoes, Suburbans, vans, etc.)
Then, they have to fly AF-1 and a decoy AF-1 and support aircraft.
Things we take for granted. What a monumental undertaking (and cost) that is.
Actually, he can. It's just very rare. There's even a policy for it: