Measurements of Pb-210 (half life of 22.3 y) at various depths down to 180 m in an ice core from an Arctic glacier, Asgardfonna, in northern Spitsbergen have been made. The activity of Pb-210 was obtained by counting alpha-rays from its daughter nuclide, Po-210 (half life of 138 d. The specific activity of Pb-210 at the surface of the glacier, 110 mBq/kg, decreased exponentially with depth to 4.72 mBq/kg at about 30 m depth. Below 30 m, the activities were nearly constant and the average value from 30 m to 180 m was 4.85 +/- 1.33 mBq/kg. This result indicates that the atmospheric Pb-210 deposit onto the glacier decays as a function of time at a rate controlled by its half life. The (y spectrometric method for the determination of Pb-210 in an ice sample and the result of the ice core dating are described in this paper.