Crawley Green Road has been closed following reports of a collision earlier.
The collision took place near the cemetery.
A Bedfordshire Police spokesman said: “We are currently in attendance at a road traffic collision in Luton. We were called at approximately 11.50am to reports of a collision between a moped and a pedestrian on Crawley Green Road.
“One person has sustained serious injuries and the road is closed while emergency services deal with the incident.”
An East of England Ambulance spokesman added: “We were called at 11.48am today to Crawley Green Road, Luton, to a report of a road traffic collision between a moped and a pedestrian.
“Two teenagers, who were on moped, had suffered serious leg and head injuries and were taken by land ambulance to Luton and Dunstable Hospital for further care.
“The pedestrian was assessed at the scene, but did not require transport to hospital.”