Photos of the jet were posted on the website avweb.com and the L.A. Daily News.
Investigators say the vandals broke into a secure area at the airport and tagged the jet around 2 a.m.
The graffiti covers a very large part of the Learjet's fuselage and says the word "flame."
The incident is considered a serious breach of the airport's security.
The investigation is being handled by the Los Angeles Police Department, Los Angeles World Airports Police and the Federal Bureau of Investigation.
