Officials said the incident occurred around 3 AM when the deceased trooper Mukesh Kumar (40) was returning after a routine patrol with his colleague.
"On return, Mukesh put his AK-47 rifle on his head and shot himself. His colleague was just ahead of him and did not get time to stop him," a senior official said.
He said Mukesh received three bullets on his temple and was rushed to the nearby LNJP Hospital where he was pronounced dead on arrival.
Singh was a resident of Alipur in Delhi and had returned from leave on December 28.
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No immediate cause could be ascertained for him taking this step, the official said.
The constable had joined the paramilitary in 1997 and was deployed to secure the Airport Metro line's New Delhi station here.
He is survived by wife and two school-going children.