We report on the observation of single colour centers in natural diamond samples emitting in the near infrared region when optically excited. Photoluminescence of these single emitters have several striking features, such as a narrow-band fully polarized emission (FWHM 2 nm) around 780 nm, a short excited-state lifetime of about 2 ns, and perfect photostability at room temperature under our excitation conditions. We present a detailed study of their photophysical properties. Development of a triggered single-photon source relying on this single colour centre is discussed in the prospect of its application to quantum key distribution.