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A superconducting nanowire single photon detector (SNSPD) system for telecommunication wavelength using a GM cryocooler was developed and its performance was verified. The cryocooler based SNSPD system can operate continuously with a 100 V AC power supply without any cryogen. The packaged SNSPD device was cooled to 2.96 K within a thermal fluctuation range of 10 mK. An SNSPD with an area of 20 times 20 mum2 showed good system detection efficiency (DE) at 100 Hz dark count rate of 2.6% and 4.5% at wavelengths of 1550 and 1310 nm, respectively. An SNSPD with an area of 10 times 10 mum2 and kinetic inductance lower than that of the large area device showed good system DE of 2.6% at a wavelength of 1550 nm. The SNSPD system could be operated for over 10 h with constant system DE and dark count rate.