Surface snow density is an important variable for the surface mass balance and energy budget. It evolves according to meteorological conditions, in particular, snowfall, wind, and temperature, but the physical processes governing atmospheric influence on snow are not fully understood. A reason is that no systematic observation is available on a continental scale. Here, we use the passive microwave observations from AMSR-E satellite to retrieve the surface snow density at Dome C on the East Antarctic Plateau. The retrieval method is based on the difference of surface reflections between horizontally and vertically polarized brightness temperatures at 37 GHz, highlighted by the computation of the polarization ratio, which is related to surface snow density. The relationship has been obtained with a microwave emission radiative transfer model (DMRT-ML). The retrieved density, approximately representative of the topmost 3 cm of the snowpack, compares well with in situ measurements. The difference between mean in situ measurements and mean retrieved density is 26.2 kg m^-3, which is within typical in situ measurement uncertainties. We apply the retrieval method to derive the time series over the period 2002-2011. The results show a marked and persistent pluri-annual decrease of about 10 kg m^-3 yr^-1, in addition to atmosphere-related seasonal, weekly, and daily density variations. This trend is confirmed by independent active microwave observations from the ENVISAT and QuikSCAT satellites, though the link to the density is more difficult to establish. However, no related pluri-annual change in meteorological conditions has been found to explain such a trend in snow density. Further work will concern the extension of the method to the continental scale.