He owns a former Qantas 707-138B since a few years. Its registered N707JT and was painted in a scheme similar to the TWA-livery of the 60s (in blue) last year.
You can find a picture on airliners.net.
Or it already could be out fitted with Stage 3 engines and all the stuff that can save the 707 fuel like that one 707 and DC-8 owned by Quiet Skies Inc Those two planes they own not only haves Stgae three engines but winglets as well.
Below is a link with some great details on Travolta's airline, including some info on his 707. Ever since I was a kid, I dreamed of flying on the 707, but they dropped out of US passenger service before I was old enough to buy my own ticket! It's great to see one of these marvelous aircraft in the hands of someone capable of looking after it.