A numerical model of the negative DC corona plasma along a thin wire in dry air is presented. The electron number density and electric field are determined from solution of the one-dimensional coupled continuity equations of charge carriers and Maxwell's equation. The electron kinetic energy distribution is determined from the spatially homogeneous Boltzmann equation. A parametric study is conducted to examine the effects of linear current density (0.1-100 muA per cm of wire length), wire radius (10-1000 mum), and air temperature (293-800 K) on the distribution of electrons and the Townsend second ionization coefficient. The results are compared to those previously determined for the positive corona discharge. In the negative corona, energetic electrons are present beyond the ionization boundary and the number of electrons is an order of magnitude greater than in the positive corona. The number of electrons increases with increasing gas temperature. The electron energy distribution does not depend on discharge polarity.