We report on the characterization of the nanowire (NW) light-emitting diodes (NW-LEDs) emitting in telecom bands incorporating InP/InAsP heterostructure in the NW pn-junction. The NW showed sharp emission lines in the low-temperature photoluminescence (PL) spectra, suggesting the formation of quantum dots (QDs) in the NW. An NW-LED operation was demonstrated at both room and low temperatures. Furthermore, a sharp emission line was also observed under the current injection, which shows a possibility of our NW-LEDs as an on-demand single-photon source.