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In order to improve the detection sensitivity of 85Kr, an anti-cosmic HPGe γ spectrometer was established and a specific Marinelli beaker was designed for 85Kr measurement. Comparing to the non-anticoincidence γ spectrum, the integral background counts rate range from 20 to 2400 keV was reduced by a factor of 5.17 using anticoincidence shielding. The minimum detectable activity of 85Kr was 10.5 Bq within 24 h measurement in standard mode and that of 3.99 Bq in anticoincidence mode. The activity concentration of atmospheric 85Kr was preliminarily measured to be an average of 1.30 Bq/m3 in Beijing and corresponding minimum detectable concentration was 0.2 Bq/m3. • An anti-cosmic HPGe γ spectrometer was established and a specific Marinelli beaker was designed for 85Kr measurement. • The minimum detectable activity of 85Kr was 3.99Bq by using the anti-cosmic HPGe γ spectrometer. • A preliminary measurement result of activity concentration of atmospheric 85Kr in Beijing was an average of 1.30 Bq/m3. [ABSTRACT FROM AUTHOR]