The charging of aerosols and the conductivity of the lower, night time atmosphere of Mars are calculated. The charge distribution of aerosols was obtained by the simultaneous solution of the ion-aerosol charge balance equations. Galactic cosmic rays are the dominant ionizing process in the night time lower atmosphere producing molecular ions and ion clusters. The ion production rates for different solar activities are considered. The ion-ion recombination rates and the ion-aerosols attachment coefficients are calculated for altitudes from 0 to 70 km. Both the steady state and time dependent concentration of charged aerosols are calculated. The conductivity produced by ion-attachment of aerosols was found to decrease by a factor of five yielding a value of about 4 W 10-12 Ohm-1 m-1 close to the surface. The effect on the conductivity of the temperature vs. altitude and the aerosol density are also estimated.