The natural radioactive nuclide, ^Pb, with a half-life of 22.3 years in snow and ice is useful for considering the origin of atmospheric aerosols and also for estimating the sedimentation rate onto a glacier. The α spectrometric method for sensitive analysis of ^Pb in ice samples and the method of ice core dating are described in this paper. Measurements of ^Pb in ice cores from the Arctic glacier, Åsgardfonna, in the Svalbard archipelagos have been made. The activity of ^Pb was obtained by counting α rays from its daughter nuclide, ^Po (half-life 138 days). The specific activity of ^Pb at the surface of the glacier, 110mBq/kg, decreased exponentially with depth to 4.72mBq/kg at about 30m depth. Below 30m, the activities were nearly constant and its average value from 30m to 180m was 4.85±1.33mBq/kg. The results indicate that the atmospheric ^Pb deposit onto a glacier decays as a function of time at a rate controlled by its half-life.