The pilot has been identified as 58-year-old Craig Maccalum of Montclair, New Jersey.
The small plane went down at an old GM plant on West Edgar Avenue shortly after it took off from Linden Airport.
The plane never got much higher than the low level buildings in the area, and crashed nose first on to the railroad tracks next to the site of the old General Motors plant, said Paul Dudley with Linden Airport.
Two people, a pilot and his student were in the plane when it went down. The student remains in the hospital in critical condition.
Maccalum is part owner of the company "Best in Flight", which has been operating out of the linden airport for about 2 years.
The manager says this is the first accident of this kind in about 6 years.
It wasn't immediately clear who was flying the aircraft at the time of the distress call, but Dudley said the plane was equipped with dual controls for training.
The plane was registered to a company in Denville, Federal Aviation Administration records showed. Dudley said the plane was operated by Best In Flight, a flight training company that has been based at Linden Airport for about two years. The company didn't immediately return a phone message seeking comment Friday.
Linden Airport is several miles south of Newark Liberty Airport and is the site of numerous training flights, Dudley said.
The train tracks where the plane landed are not used by New Jersey Transit and didn't affect commuter service, a railroad spokesman said. The crash occurred in an area that NJ Transit has been considering as an emergency storage area for trains to protect them from possible flooding as a response to Superstorm Sandy, spokesman John Durso Jr. said.
(Some information from the Associated Press)