Officials said the incident occurred about 3 am when a fire was reported from the 4th floor of the Electronic Data Processing centre of the force located in R K Puram area of the national capital.
Fire officials said seven tenders were rushed to the spot and the fire fighting operation ended early morning.
The head constable, who was sleeping inside the building, has been killed.
"The jawan was not responding to evacuation calls and it is understood he must be in deep sleep," an official said.
Fire officials said the entire floor was gutted in the fire and many records and electronic gadgets are believed to have been gutted.
The EDP cell of the force, under the training wing, deals with record management of pay and other emoluments of CRPF personnel.
Senior officials of the force have reached the spot for an assessment and enumeration of the damage, they said.